A347133 - OEIS

%I #11 Aug 27 2021 05:30:36

%S 0,0,0,1,0,2,0,6,1,2,0,16,0,2,2,24,0,19,0,20,2,2,0,72,1,2,9,24,0,40,0,

%T 80,2,2,2,111,0,2,2,96,0,48,0,32,25,2,0,256,1,29,2,36,0,117,2,120,2,2,

%U 0,244,0,2,29,240,2,64,0,44,2,56,0,446,0,2,31,48,2,72,0,352,54,2,0,308,2,2,2,168,0,304,2,56

%N a(n) = Sum_{d|n} A003415(n/d) * A069359(d).

%C Dirichlet convolution of A003415 (arithmetic derivative) with A069359.

%C Dirichlet convolution of A001221 (omega, number of distinct prime factors of n) with A347131.

%H Antti Karttunen, <a href="/A347133/b347133.txt">Table of n, a(n) for n = 1..10080</a>

%H Antti Karttunen, <a href="/A347133/a347133.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%F a(n) = Sum_{d|n} A003415(n/d) * A069359(d).

%F a(n) = Sum_{d|n} A001221(n/d) * A347131(d).

%o (PARI)

%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

%o A069359(n) = (n*sumdiv(n, d, isprime(d)/d)); \\ From A069359

%o A347133(n) = sumdiv(n,d,A003415(n/d)*A069359(d));

%Y Cf. A001221, A003415, A069359, A347131.

%Y Cf. also A300251, A305809, A347132, A347134, A347135.

%K nonn

%O 1,6

%A _Antti Karttunen_, Aug 23 2021