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

Author

René-Louis Clerc, Jan 10 2024

Keywords

• base
• nonn
• fini
• more

Comments

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

Examples

			430080 = 724856_9, (7+2+4+8+5+6)*(7*2*4*8*5*6) = 32*13440 = 430080.
		

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

Programs

Mathematica

Select[Range[5*10^6],Total[IntegerDigits[#,9]]*Fold[Times,1,IntegerDigits[#,9]]==#&] (* James C. McMahon, Jan 30 2024 *)

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, ", ")))