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A305809 Dirichlet convolution of A003415 (Arithmetic derivative) with itself. 4


%S 0,0,0,1,0,2,0,8,1,2,0,18,0,2,2,40,0,22,0,22,2,2,0,96,1,2,12,26,0,40,

%T 0,160,2,2,2,147,0,2,2,128,0,48,0,34,28,2,0,400,1,34,2,38,0,156,2,160,

%U 2,2,0,276,0,2,32,560,2,64,0,46,2,56,0,680,0,2,36,50,2,72,0,560,90,2,0,348,2,2,2,224,0,346,2,58,2,2,2,1440,0,46,40,267,0,88

%N Dirichlet convolution of A003415 (Arithmetic derivative) with itself.

%H Antti Karttunen, <a href="/A305809/b305809.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = Sum_{d|n} A003415(n/d)*A003415(d).

%o (PARI)

%o A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415

%o A305809(n) = sumdiv(n,d,A003415(n/d)*A003415(d));

%Y Cf. A003415, A300251, A300252.

%Y Cf. A008578 (positions of 0's), A001248 (of 1's), A006881 (of 2's).

%K nonn

%O 1,6

%A _Antti Karttunen_, Jun 13 2018

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Last modified May 24 15:25 EDT 2019. Contains 323532 sequences. (Running on oeis4.)