A367070 Numbers k such that k = (product of nonzero digits) * (sum of digits) for the digits of k in base 7.

1, 16, 128, 250, 480, 864, 21600, 62208, 73728

Offset: 1

Author

René-Louis Clerc, Jan 10 2024

Keywords

• base
• nonn
• fini
• more

Comments

There is a finite number of such numbers; we only calculated the terms in [1, 10^10] (Property 1' of Clerc).

Examples

			21600 = 116655_7, (1+1+6+6+5+5)*(1*1*6*6*5*5) = 24*900 = 21600.
		

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[7^7], #1 == Times @@ DeleteCases[#2, 0]*Total[#2] & @@ {#, IntegerDigits[#, 7]} &] (* Michael De Vlieger, Mar 25 2024 *)

PARI

isok(k, b) = my(d=select(x->(x>0), digits(k,b))); vecprod(d)*vecsum(d) == k;
for (k=1, 10^5, if (isok(k, 7), print1(k, ", ")))