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A370251
Base-12 numbers k such that k = (product of nonzero digits of k) * (sum of digits of k) (written in base 10).
0
1, 176, 231, 495, 7040
OFFSET
1,2
COMMENTS
There are only finitely many such numbers (Property 1' of Clerc).
LINKS
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, ", ")))
KEYWORD
base,nonn,fini,more
AUTHOR
René-Louis Clerc, Feb 13 2024
STATUS
approved