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

1,2

Comments

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

Links

Table of n, a(n) for n=1..9.

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

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

Mathematica

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

Prog

(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, ", ")))

Crossrefs

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

Sequence in context: A133111 A268998 A253319 * A291460 A004017 A167471

Adjacent sequences: A367067 A367068 A367069 * A367071 A367072 A367073

Keyword

base,nonn,fini,more

Author

René-Louis Clerc, Jan 10 2024

Status

approved