A144368 Shifts 4 places left under Dirichlet convolution.

1, 1, 1, 1, 1, 2, 2, 3, 2, 6, 4, 8, 5, 14, 8, 22, 10, 32, 18, 51, 20, 72, 36, 116, 44, 152, 72, 258, 89, 314, 148, 548, 178, 660, 296, 1146, 364, 1340, 596, 2380, 728, 2716, 1202, 4880, 1456, 5508, 2404, 9912, 2932, 11088, 4808, 20128, 5868, 22276, 9636

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

4th column of A144374. Cf. A000005.

Programs

Maple

k:= 4: 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..55);

Mathematica

dck[b_, c_][n_, k_] := dck[b, c][n, k] = Sum[b[d, k]*c[n/d, k], {d, If[n < 0, {}, Divisors[n]]}];
B = dck[T, T];
T[n_, k_] := If[n <= k, 1, B[n - k, k]];
a[n_] := T[n, 4];
Array[a, 55] (* Jean-François Alcover, Jun 11 2018, after Alois P. Heinz *)

Formula

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