A370251 Base-12 numbers k such that k = (product of nonzero digits of k) * (sum of digits of k) (written in base 10).

1, 176, 231, 495, 7040

Offset: 1

Author

René-Louis Clerc, Feb 13 2024

Keywords

• base
• nonn
• fini
• more

Comments

There are only finitely many such numbers (Property 1' of Clerc).

Examples

			231 = 173_12, (1*7*3)*(1+7+3) = 21*11 = 231.
		

Links

• René-Louis Clerc, Quelques nombres de Niven-Harshad particuliers, 2023.
• René-Louis Clerc, Nombres S+P, maxSP, minSP et |P-S|, hal-04507547 [math.nt], 2024. (In French)

Crossrefs

Cf. A366832, A367070, A066282, A062331, A023651, A038364, A038369, A062237.

Programs

Mathematica

Select[Range[5*10^4], Total[IntegerDigits[#, 12]]*Fold[Times, 1, Select[IntegerDigits[#, 12],#>0&]]==#&] (* James C. McMahon, Feb 14 2024 *)

PARI

isok(k, b) = my(d=select(x->(x>0), digits(k, b))); vecprod(d)*vecsum(d) == k;
for (k=0, 10^10, if (isok(k, 12), print1(k, ", ")))