A099542 Rhonda numbers to base 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, 118465, 133857, 148653, 154462, 161785

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 21 2004

Keywords

• base
• nice
• nonn

Comments

An integer m is a Rhonda number to base b if the product of its digits in base b equals b*(sum of prime factors of m (taken with multiplicity)).

Does every Rhonda number to base 10 contain at least one 5? - Howard Berman (howard_berman(AT)hotmail.com), Oct 22 2008

Yes, every Rhonda number m to base 10 contains at least one 5 and also one even digit, otherwise A007954(m) mod 10 > 0. - Reinhard Zumkeller, Dec 01 2012

Examples

			1568 has prime factorization 2^5 * 7^2. Sum of prime factors = 2*5 + 7*2 = 24. Product of digits of 1568 = 1*5*6*8 = 240 = 10*24, hence 1568 is a Rhonda number to base 10.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000 (first 180 terms from Harvey P. Dale)
• Kevin Brown, Infinitely Many Rhondas.
• Giovanni Resta, Rhonda numbers the 64507 base-10 Rhonda numbers up to 10^12.
• Walter Schneider, Rhonda Numbers.
• Eric Weisstein's World of Mathematics, Rhonda Number.

Crossrefs

Cf. Rhonda numbers to other bases: A100968 (base 4), A100969 (base 6), A100970 (base 8), A100973 (base 9), 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 A255880.

Cf. A001414, A027746, A007954.

Column k=5 of A291925.

Programs

Haskell

import Data.List (unfoldr); import Data.Tuple (swap)
a099542 n = a099542_list !! (n-1)
a099542_list = filter (rhonda 10) [1..]
rhonda b x = a001414 x * b == product (unfoldr
       (\z -> if z == 0 then Nothing else Just $ swap $ divMod z b) x)
-- Reinhard Zumkeller, Mar 05 2015, Dec 01 2012

Mathematica

Select[Range[200000],10Total[Times@@@FactorInteger[#]]==Times@@ IntegerDigits[ #]&] (* Harvey P. Dale, Oct 16 2011 *)

Formula

A007954(a(n)) = 10 * A001414(a(n)).