OFFSET
1,2
COMMENTS
There is a finite number of such numbers (Property 1' of Clerc).
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)
EXAMPLE
430080 = 724856_9, (7+2+4+8+5+6)*(7*2*4*8*5*6) = 32*13440 = 430080.
MATHEMATICA
Select[Range[5*10^6], Total[IntegerDigits[#, 9]]*Fold[Times, 1, IntegerDigits[#, 9]]==#&] (* James C. McMahon, Jan 30 2024 *)
PROG
(PARI) isok(k, b) = my(d=select(x->(x>0), digits(k, b))); vecprod(d)*vecsum(d) == k;
for (k=1, 10^7, if (isok(k, 9), print1(k, ", ")))
CROSSREFS
KEYWORD
base,nonn,fini,more
AUTHOR
René-Louis Clerc, Jan 10 2024
STATUS
approved