Rhonda number

An integer n is a Rhonda number to base b if the product of its digits in base b equals b×sum of prime factors of n (including multiplicity).

The base 10 Rhonda numbers are 1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662, 33475, 34935, 35581, 45951, 47265, 47594, ... (sequence A099542 in the OEIS), Rhonda numbers only exist in composite bases, since if b is prime, then the product of the digits of any number n in base b cannot be divisible by b, and if b = 1, then the product of the digits of any number n is 1, thus the sum of prime factors of n must be 1, but that is impossible.

Other bases

Base	Rhonda numbers	OEIS sequence
4	10206, 11935, 12150, 16031, 45030, 94185, 113022, 114415, 191149, 244713, 259753, 374782, 392121, 503773, 649902, 703326, 716250, 764526, 883630, 884446, 912766, 980694, 980837, ...	A100968
6	855, 1029, 3813, 5577, 7040, 7304, 15104, 19136, 35350, 36992, 41031, 42009, 60368, 65536, 67821, 76880, 84525, 90601, 122831, 131175, 154570, 162565, 184009, 184585, 196504, ...	A100969
8	1836, 6318, 6622, 10530, 14500, 14739, 17655, 18550, 25398, 25956, 30562, 39215, 39325, 50875, 51429, 52887, 55611, 56420, 58548, 59731, 60604, 72358, 74620, 76581, 78780, 81370, 84180, 85949, ...	A100970
9	15540, 21054, 25331, 44360, 44660, 44733, 47652, 50560, 54944, 76857, 77142, 83334, 83694, 96448, 97944, 106575, 108273, 117624, 125952, 138966, 141204, 144236, ...	A100973
10	1568, 2835, 4752, 5265, 5439, 5664, 5824, 5832, 8526, 12985, 15625, 15698, 19435, 25284, 25662, 33475, 34935, 35581, 45951, 47265, 47594, 52374, 53176, 53742, 54479, 55272, 56356, 56718, 95232, ...	A099542
12	560, 800, 3993, 4425, 4602, 4888, 7315, 8296, 9315, 11849, 12028, 13034, 14828, 15052, 16264, 18511, 18906, 25619, 25875, 27176, 32742, 37264, 37523, 46035, ...	A100971
14	11475, 18655, 20565, 29631, 31725, 45387, 58404, 58667, 59950, 63945, 67525, 68904, 91245, 99603, 125543, 135196, 141141, 148645, 149575, 168270, 175577, ...	A100972
15	2392, 2472, 11468, 15873, 17424, 18126, 19152, 20079, 24388, 30758, 31150, 33004, 33550, 37925, 39483, 42550, 44714, 58870, 59605, 66950, 70182, 71485, 71709, 85557, 85848, 86241, 86591, 92150, ...	A100974
16	1000, 1134, 6776, 15912, 19624, 20043, 20355, 23946, 26296, 29070, 31906, 32292, 34236, 34521, 36465, 39066, 50055, 50986, 52341, 54340, 58088, 59541, 75867, 85870, 87150, 88182, 93058, 95944, 99674, ...	A100975

560 is the smallest number that is Rhonda number in some base (namely, base 12), and 1000 is the smallest number that is Rhonda number in two bases (namely, base 16 and base 36).

See also

• Sum-product number

External links

• Weisstein, Eric W. "Rhonda Number". MathWorld.
• Walter Schneider, Rhonda Numbers
• Giovanni Resta, Rhonda number

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📰 Article(s) of the same category(ies)

• Smarandache number
• Missing-digit sum

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