A347963 - OEIS

%I #7 Oct 15 2021 21:33:37

%S 0,1,1,3,1,7,1,7,3,9,1,18,1,11,10,15,1,18,1,24,12,15,1,40,3,17,8,30,1,

%T 54,1,31,16,21,14,45,1,23,18,54,1,68,1,42,27,27,1,84,3,24,22,48,1,48,

%U 18,68,24,33,1,132,1,35,33,63,20,96,1,60,28,90,1,99,1,41,27,66,20,110,1,114,22,45,1,168,24,47

%N Dirichlet convolution of A342001 with A003557.

%H Antti Karttunen, <a href="/A347963/b347963.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n) = Sum_{d|n} A003557(d) * A342001(n/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 A003557(n) = (n/factorback(factorint(n)[, 1]));

%o A342001(n) = (A003415(n) / A003557(n));

%o A347963(n) = sumdiv(n,d,A003557(n/d)*A342001(d));

%Y Cf. A003415, A003557, A342001.

%Y Cf. also A347961.

%K nonn

%O 1,4

%A _Antti Karttunen_, Sep 24 2021