A366832 Numbers k such that k = (product of nonzero digits) * (sum of digits) for the digits of k in base 9.

1, 12, 1536, 172032, 430080, 4014080

Offset

1,2

Comments

There is a finite number of such numbers (Property 1' of Clerc).

Links

Table of n, a(n) for n=1..6.

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

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

Sequence in context: A015096 A271434 A299694 * A160237 A013474 A013515

Adjacent sequences: A366829 A366830 A366831 * A366833 A366834 A366835

Keyword

base,nonn,fini,more

Author

René-Louis Clerc, Jan 10 2024

Status

approved