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A144367 Shifts 3 places left under Dirichlet convolution.

%I A144367 #14 May 09 2019 18:17:06
%S A144367 1,1,1,1,2,2,3,4,6,6,10,13,16,20,32,32,46,68,73,92,152,146,200,310,
%T A144367 312,400,658,628,832,1328,1302,1664,2740,2604,3400,5500,5300,6812,
%U A144367 11178,10600,13770,22388,21412,27540,45132,42824,55392,90352,86048,110784
%N A144367 Shifts 3 places left under Dirichlet convolution.
%H A144367 Alois P. Heinz, <a href="/A144367/b144367.txt">Table of n, a(n) for n = 1..1000</a>
%H A144367 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%F A144367 G.f.: x + x^2 + x^3 * (1 + Sum_{i>=1} Sum_{j>=1} a(i)*a(j)*x^(i*j)). - _Ilya Gutkovskiy_, May 09 2019
%p A144367 k:= 3: 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 A144367 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 A144367 B = dck[T, T];
%t A144367 T[n_, k_] := If[n <= k, 1, B[n - k, k]];
%t A144367 a[n_] := T[n, 3];
%t A144367 Array[a, 55] (* _Jean-François Alcover_, Jun 11 2018, after _Alois P. Heinz_ *)
%Y A144367 3rd column of A144374. Cf. A000005.
%K A144367 eigen,nonn
%O A144367 1,5
%A A144367 _Alois P. Heinz_, Sep 18 2008