A100973 Integers that are Rhonda numbers to base 9.

15540, 21054, 25331, 44360, 44660, 44733, 47652, 50560, 54944, 76857, 77142, 83334, 83694, 96448, 97944, 106575, 108273, 117624, 125952, 138966, 141204, 144236, 153318, 158417, 159424, 188529, 188598, 189350, 192000, 192126, 196652, 202350, 203320, 205390, 246675, 247632

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 25 2004

Keywords

• easy
• nonn
• base

Comments

See sequence A099542 for definition of Rhonda numbers and for some links.

Examples

			The product of the base 9 digits of 15540 is 2*3*2*7*6=504, the sum of the prime factors of 15540 is 2*2+3+5+7+37=56 and 504=9*56. So 15540 is a Rhonda number to base 9.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Rhonda Number

Crossrefs

Cf. Rhonda numbers to other bases: A100968 (base 4), A100969 (base 6), A100970 (base 8), A099542 (base 10), A100971 (base 12), A100972 (base 14), A100974 (base 15), A100975 (base 16), A255735 (base 18), A255732 (base 20), A255736 (base 30), A255731 (base 60), see also A255872.

Cf. A001414, A027746, A007095, subsequence of A255808.

Column k=4 of A291925.

Programs

Haskell

a100973 n = a100973_list !! (n-1)
a100973_list = filter (rhonda 9) a255808_list
-- Function rhonda as in A099542.
-- Reinhard Zumkeller, Mar 08 2015

Mathematica

A100973Q[k_] := Times @@ IntegerDigits[k, 9] == 9*Total[Times @@@ FactorInteger[k]];
Select[Range[250000], A100973Q] (* Paolo Xausa, Jul 01 2025 *)