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A099542 Rhonda numbers to base 10.

%I A099542 #43 Feb 16 2025 08:32:55
%S A099542 1568,2835,4752,5265,5439,5664,5824,5832,8526,12985,15625,15698,19435,
%T A099542 25284,25662,33475,34935,35581,45951,47265,47594,52374,53176,53742,
%U A099542 54479,55272,56356,56718,95232,118465,133857,148653,154462,161785
%N A099542 Rhonda numbers to base 10.
%C A099542 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)).
%C A099542 Does every Rhonda number to base 10 contain at least one 5? - Howard Berman (howard_berman(AT)hotmail.com), Oct 22 2008
%C A099542 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
%H A099542 Reinhard Zumkeller, <a href="/A099542/b099542.txt">Table of n, a(n) for n = 1..1000</a> (first 180 terms from Harvey P. Dale)
%H A099542 Kevin Brown, <a href="http://www.mathpages.com/home/kmath007/kmath007.htm">Infinitely Many Rhondas</a>.
%H A099542 Giovanni Resta, <a href="http://www.numbersaplenty.com/set/Rhonda_number/">Rhonda numbers</a> the 64507 base-10 Rhonda numbers up to 10^12.
%H A099542 Walter Schneider, <a href="http://web.archive.org/web/2004/www.wschnei.de/digit-related-numbers/rhonda-numbers.html">Rhonda Numbers</a>.
%H A099542 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RhondaNumber.html">Rhonda Number</a>.
%F A099542 A007954(a(n)) = 10 * A001414(a(n)).
%e A099542 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.
%t A099542 Select[Range[200000],10Total[Times@@@FactorInteger[#]]==Times@@ IntegerDigits[ #]&] (* _Harvey P. Dale_, Oct 16 2011 *)
%o A099542 (Haskell)
%o A099542 import Data.List (unfoldr); import Data.Tuple (swap)
%o A099542 a099542 n = a099542_list !! (n-1)
%o A099542 a099542_list = filter (rhonda 10) [1..]
%o A099542 rhonda b x = a001414 x * b == product (unfoldr
%o A099542        (\z -> if z == 0 then Nothing else Just $ swap $ divMod z b) x)
%o A099542 -- _Reinhard Zumkeller_, Mar 05 2015, Dec 01 2012
%Y A099542 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.
%Y A099542 Cf. A001414, A027746, A007954.
%Y A099542 Column k=5 of A291925.
%K A099542 base,nice,nonn
%O A099542 1,1
%A A099542 Mark Hudson (mrmarkhudson(AT)hotmail.com), Oct 21 2004