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A144372 Shifts 8 places left under Dirichlet convolution. 2

%I

%S 1,1,1,1,1,1,1,1,1,2,2,3,2,4,2,4,3,6,4,10,4,10,6,11,6,16,8,26,10,24,

%T 12,32,13,36,18,62,20,58,24,74,30,78,38,145,40,124,52,174,60,174,76,

%U 314,86,260,104,386,121,364,158,664,172,550,212,834,250,748,316,1410,344,1124

%N Shifts 8 places left under Dirichlet convolution.

%H Alois P. Heinz, <a href="/A144372/b144372.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 + x^5 + x^6 + x^7 + x^8 * (1 + Sum_{i>=1} Sum_{j>=1} a(i)*a(j)*x^(i*j)). - _Ilya Gutkovskiy_, May 09 2019

%p k:= 8: 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);

%Y 8th column of A144374. Cf. A000005.

%K eigen,nonn

%O 1,10

%A _Alois P. Heinz_, Sep 18 2008

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Last modified May 8 15:03 EDT 2021. Contains 343666 sequences. (Running on oeis4.)