A338854 - OEIS

%I #6 Nov 13 2020 14:22:33

%S 1,1,2,3,1,1,2,3,2,2,4,6,3,3,6,9,1,1,2,3,1,1,2,3,2,2,4,6,3,3,6,9,2,2,

%T 4,6,2,2,4,6,4,4,8,12,6,6,12,18,3,3,6,9,3,3,6,9,6,6,12,18,9,9,18,27,1,

%U 1,2,3,1,1,2,3,2,2,4,6,3,3,6,9,1

%N Product of the nonzero digits of (n written in base 4).

%F G.f. A(x) satisfies: A(x) = (1 + x + 2*x^2 + 3*x^3) * A(x^4).

%F a(n) = 2^A160382(n) * 3^A160383(n).

%t Table[Times @@ DeleteCases[IntegerDigits[n, 4], 0], {n, 0, 80}]

%t nmax = 80; A[_] = 1; Do[A[x_] = (1 + x + 2 x^2 + 3 x^3) A[x^4] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

%o (PARI) a(n) = vecprod(select(x->x, digits(n, 4))); \\ _Michel Marcus_, Nov 12 2020

%Y Cf. A007090, A051801, A117592, A160382, A160383, A309954.

%K nonn,base

%O 0,3

%A _Ilya Gutkovskiy_, Nov 12 2020