A144368 - OEIS

%I #14 May 09 2019 18:17:18

%S 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,

%T 258,89,314,148,548,178,660,296,1146,364,1340,596,2380,728,2716,1202,

%U 4880,1456,5508,2404,9912,2932,11088,4808,20128,5868,22276,9636

%N Shifts 4 places left under Dirichlet convolution.

%H Alois P. Heinz, <a href="/A144368/b144368.txt">Table of n, a(n) for n = 1..1000</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F 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

%p 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);

%t dck[b_, c_][n_, k_] := dck[b, c][n, k] = Sum[b[d, k]*c[n/d, k], {d, If[n < 0, {}, Divisors[n]]}];

%t B = dck[T, T];

%t T[n_, k_] := If[n <= k, 1, B[n - k, k]];

%t a[n_] := T[n, 4];

%t Array[a, 55] (* _Jean-François Alcover_, Jun 11 2018, after _Alois P. Heinz_ *)

%Y 4th column of A144374. Cf. A000005.

%K eigen,nonn

%O 1,6

%A _Alois P. Heinz_, Sep 18 2008