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A338882 Product of the nonzero digits of (n written in base 9).

%I A338882 #10 Oct 08 2021 15:29:20
%S A338882 1,1,2,3,4,5,6,7,8,1,1,2,3,4,5,6,7,8,2,2,4,6,8,10,12,14,16,3,3,6,9,12,
%T A338882 15,18,21,24,4,4,8,12,16,20,24,28,32,5,5,10,15,20,25,30,35,40,6,6,12,
%U A338882 18,24,30,36,42,48,7,7,14,21,28,35,42,49,56,8,8,16,24,32,40,48,56,64
%N A338882 Product of the nonzero digits of (n written in base 9).
%H A338882 Harvey P. Dale, <a href="/A338882/b338882.txt">Table of n, a(n) for n = 0..1000</a>
%F A338882 G.f. A(x) satisfies: A(x) = (1 + x + 2*x^2 + 3*x^3 + 4*x^4 + 5*x^5 + 6*x^6 + 7*x^7 + 8*x^8) * A(x^9).
%t A338882 Table[Times @@ DeleteCases[IntegerDigits[n, 9], 0], {n, 0, 80}]
%t A338882 nmax = 80; A[_] = 1; Do[A[x_] = (1 + x + 2 x^2 + 3 x^3 + 4 x^4 + 5 x^5 + 6 x^6 + 7 x^7 + 8 x^8) A[x^9] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
%t A338882 Table[Times@@(IntegerDigits[n,9]/.(0->1)),{n,0,80}] (* _Harvey P. Dale_, Oct 08 2021 *)
%o A338882 (PARI) a(n) = vecprod(select(x->x, digits(n, 9))); \\ _Michel Marcus_, Nov 14 2020
%Y A338882 Product of the nonzero digits of (n written in base k): A000012 (k = 2), A117592 (k = 3), A338854 (k = 4), A338803 (k = 5),  A338863 (k = 6), A338880 (k = 7), A338881 (k = 8), this sequence (k = 9), A051801 (k = 10).
%Y A338882 Cf. A007095, A309788.
%K A338882 nonn,base
%O A338882 0,3
%A A338882 _Ilya Gutkovskiy_, Nov 13 2020