A347954 - OEIS

%I #8 Oct 15 2021 21:37:27

%S 0,1,1,3,1,8,1,6,4,11,1,20,1,14,13,10,1,26,1,29,16,20,1,37,5,23,12,38,

%T 1,81,1,15,22,29,19,62,1,32,25,55,1,106,1,56,48,38,1,59,6,48,31,65,1,

%U 74,25,73,34,47,1,191,1,50,61,21,28,156,1,83,40,151,1,112,1,59,60,92,28,181,1,89,34,65,1,254,34

%N Dirichlet convolution of A003602 with A342001.

%H Antti Karttunen, <a href="/A347954/b347954.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n) = Sum_{d|n} A003602(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 A003602(n) = (1+(n>>valuation(n,2)))/2;

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

%o A347954(n) = sumdiv(n,d,A003602(d)*A342001(n/d));

%Y Cf. A003415, A003557, A003602, A342001.

%Y Cf. also A347234, A347955, A347956.

%K nonn

%O 1,4

%A _Antti Karttunen_, Sep 20 2021