A144373 Shifts 9 places left under Dirichlet convolution.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 2, 4, 2, 4, 3, 4, 4, 8, 6, 6, 10, 7, 8, 10, 8, 12, 18, 16, 12, 28, 15, 22, 22, 22, 24, 48, 32, 30, 60, 38, 46, 57, 44, 56, 102, 76, 60, 142, 76, 108, 124, 100, 112, 234, 153, 136, 292, 174, 216, 276, 204, 246, 476, 330, 272, 642, 348, 464

Offset: 1

Author

Alois P. Heinz, Sep 18 2008

Keywords

• eigen
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000
• N. J. A. Sloane, Transforms

Crossrefs

9th column of A144374. Cf. A000005.

Programs

Maple

k:= 9: with(numtheory): dck:= proc(b,c) proc(n, k) option remember; add(b(d,k) *c(n/d,k), d=`if`(n<0,{}, divisors(n))) end end: B:= dck(T,T): T:= (n, k)-> if n<=k then 1 else B(n-k, k) fi: a:= n-> T(n,k): seq(a(n), n=1..80);

Formula

G.f.: x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 * (1 + Sum_{i>=1} Sum_{j>=1} a(i)*a(j)*x^(i*j)). - Ilya Gutkovskiy, May 09 2019