A338854 Product of the nonzero digits of (n written in base 4).

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, 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, 1, 2, 3, 1, 1, 2, 3, 2, 2, 4, 6, 3, 3, 6, 9, 1

Offset

0,3

Links

Table of n, a(n) for n=0..80.

Formula

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

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

Mathematica

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

Prog

(PARI) a(n) = vecprod(select(x->x, digits(n, 4))); \\ Michel Marcus, Nov 12 2020

Crossrefs

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

Sequence in context: A190593 A276336 A212811 * A330957 A352924 A327192

Adjacent sequences: A338851 A338852 A338853 * A338855 A338856 A338857

Keyword

nonn,base

Author

Ilya Gutkovskiy, Nov 12 2020

Status

approved