I first reviewed Rhonda Numbers in an eponymous post on the 16th October 2018. Read that post to find out what defines such numbers. Today, upon turning 28280 days old, I was reminded of them again because this number is a member of OEIS A255731:
The program that I wrote back then only covered bases from 2 to 36 so I got Gemini to write a new SageMath program that would accommodate every base. Here is what is generated as output when asked to find all Rhonda numbers in base 60 in the range up to one million (permalink):
3348, 3510, 6750, 17430, 18750, 18876, 18944, 19475, 20564, 21312, 26550, 28280, 37230, 38396, 43940, 48042, 77770, 88270, 91224, 97470, 108882, 111403, 120046, 123630, 181996, 182646, 235467, 253460, 260429, 264735, 278675, 289161, 295960, 296055, 306642, 324394, 325593, 337040, 348641, 361221, 377130, 378444, 398274, 411342, 412930, 441048, 444405, 450528, 453470, 458136, 469098, 499533, 503310, 517803, 533731, 534795, 541807, 547515, 566754, 598695, 612374, 612870, 626535, 630410, 656370, 656750, 667491, 670548, 684456, 701765, 703304, 705256, 706275, 709475, 720279, 750225, 757576, 762745, 765245, 809107, 812658, 821106, 877300, 880045, 881454, 915348, 927303, 929830, 930304, 936573, 936675, 967509, 972196, 973549, 984485, 986895, 998430
I also realised that I hadn't included the identification of Rhonda numbers in my daily number analysis and that deficiency has now been remedied. Here the output of the program that I got Gemini to write for the input 29280 (permalink):
28280 : determination of whether it is a Rhonda number in a given base
--- Evaluating 28280 in Base 60 ---
1. Base-60 Digits: [7, 51, 20]
2. Digit Product: 7 * 51 * 20 = 7140
3. Prime Factorization: 2^3 * 5 * 7 * 101
4. Sum of Factors: 2 + 2 + 2 + 5 + 7 + 101 = 119
5. Target Equation (Base * Sum): 60 * 119 = 7140
RESULT: True. 28280 IS a Rhonda number in base 60.
I've set the range of bases to be investigate to 100,000 so that even a number like 889200 with is a Rhonda number in TEN different bases has an accurate output:
--- Evaluating 889200 in Base 1512 ---
1. Base-1512 Digits: [588, 144]
2. Digit Product: 588 * 144 = 84672
3. Prime Factorization: 2^4 * 3^2 * 5^2 * 13 * 19
4. Sum of Factors: 2 + 2 + 2 + 2 + 3 + 3 + 5 + 5 + 13 + 19 = 56
5. Target Equation (Base * Sum): 1512 * 56 = 84672
RESULT: True. 889200 IS a Rhonda number in base 1512.
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--- Evaluating 889200 in Base 2760 ---
1. Base-2760 Digits: [322, 480]
2. Digit Product: 322 * 480 = 154560
3. Prime Factorization: 2^4 * 3^2 * 5^2 * 13 * 19
4. Sum of Factors: 2 + 2 + 2 + 2 + 3 + 3 + 5 + 5 + 13 + 19 = 56
5. Target Equation (Base * Sum): 2760 * 56 = 154560
RESULT: True. 889200 IS a Rhonda number in base 2760.
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--- Evaluating 889200 in Base 5160 ---
1. Base-5160 Digits: [172, 1680]
2. Digit Product: 172 * 1680 = 288960
3. Prime Factorization: 2^4 * 3^2 * 5^2 * 13 * 19
4. Sum of Factors: 2 + 2 + 2 + 2 + 3 + 3 + 5 + 5 + 13 + 19 = 56
5. Target Equation (Base * Sum): 5160 * 56 = 288960
RESULT: True. 889200 IS a Rhonda number in base 5160.
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--- Evaluating 889200 in Base 7904 ---
1. Base-7904 Digits: [112, 3952]
2. Digit Product: 112 * 3952 = 442624
3. Prime Factorization: 2^4 * 3^2 * 5^2 * 13 * 19
4. Sum of Factors: 2 + 2 + 2 + 2 + 3 + 3 + 5 + 5 + 13 + 19 = 56
5. Target Equation (Base * Sum): 7904 * 56 = 442624
RESULT: True. 889200 IS a Rhonda number in base 7904.
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--- Evaluating 889200 in Base 9400 ---
1. Base-9400 Digits: [94, 5600]
2. Digit Product: 94 * 5600 = 526400
3. Prime Factorization: 2^4 * 3^2 * 5^2 * 13 * 19
4. Sum of Factors: 2 + 2 + 2 + 2 + 3 + 3 + 5 + 5 + 13 + 19 = 56
5. Target Equation (Base * Sum): 9400 * 56 = 526400
RESULT: True. 889200 IS a Rhonda number in base 9400.
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--- Evaluating 889200 in Base 10032 ---
1. Base-10032 Digits: [88, 6384]
2. Digit Product: 88 * 6384 = 561792
3. Prime Factorization: 2^4 * 3^2 * 5^2 * 13 * 19
4. Sum of Factors: 2 + 2 + 2 + 2 + 3 + 3 + 5 + 5 + 13 + 19 = 56
5. Target Equation (Base * Sum): 10032 * 56 = 561792
RESULT: True. 889200 IS a Rhonda number in base 10032.
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--- Evaluating 889200 in Base 11440 ---
1. Base-11440 Digits: [77, 8320]
2. Digit Product: 77 * 8320 = 640640
3. Prime Factorization: 2^4 * 3^2 * 5^2 * 13 * 19
4. Sum of Factors: 2 + 2 + 2 + 2 + 3 + 3 + 5 + 5 + 13 + 19 = 56
5. Target Equation (Base * Sum): 11440 * 56 = 640640
RESULT: True. 889200 IS a Rhonda number in base 11440.
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--- Evaluating 889200 in Base 12920 ---
1. Base-12920 Digits: [68, 10640]
2. Digit Product: 68 * 10640 = 723520
3. Prime Factorization: 2^4 * 3^2 * 5^2 * 13 * 19
4. Sum of Factors: 2 + 2 + 2 + 2 + 3 + 3 + 5 + 5 + 13 + 19 = 56
5. Target Equation (Base * Sum): 12920 * 56 = 723520
RESULT: True. 889200 IS a Rhonda number in base 12920.
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--- Evaluating 889200 in Base 14136 ---
1. Base-14136 Digits: [62, 12768]
2. Digit Product: 62 * 12768 = 791616
3. Prime Factorization: 2^4 * 3^2 * 5^2 * 13 * 19
4. Sum of Factors: 2 + 2 + 2 + 2 + 3 + 3 + 5 + 5 + 13 + 19 = 56
5. Target Equation (Base * Sum): 14136 * 56 = 791616
RESULT: True. 889200 IS a Rhonda number in base 14136.
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--- Evaluating 889200 in Base 15080 ---
1. Base-15080 Digits: [58, 14560]
2. Digit Product: 58 * 14560 = 844480
3. Prime Factorization: 2^4 * 3^2 * 5^2 * 13 * 19
4. Sum of Factors: 2 + 2 + 2 + 2 + 3 + 3 + 5 + 5 + 13 + 19 = 56
5. Target Equation (Base * Sum): 15080 * 56 = 844480
RESULT: True. 889200 IS a Rhonda number in base 15080.
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