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

1,2

Comments

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

Links

Table of n, a(n) for n=1..5.

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)

Example

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

Mathematica

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

Prog

(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, ", ")))

Crossrefs

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

Sequence in context: A261678 A136603 A114824 * A305062 A342452 A336026

Adjacent sequences: A370248 A370249 A370250 * A370252 A370253 A370254

Keyword

base,nonn,fini,more

Author

René-Louis Clerc, Feb 13 2024

Status

approved