A378607 - OEIS

%I #9 Dec 11 2024 15:03:46

%S 1,0,-1,-2,-1,0,-3,-6,-7,0,-1,2,-3,0,1,-14,-1,0,-3,2,3,0,-5,6,-11,0,

%T -25,6,-1,0,-5,-30,1,0,3,14,-3,0,3,6,-1,0,-3,2,7,0,-5,14,-31,0,1,6,-5,

%U 0,1,18,3,0,-1,-2,-5,0,21,-62,3,0,-3,2,5,0,-1,42,-5,0,11,6,3,0,-3,14,-79,0,-5,-6,1,0,1,6,-7,0,9,10

%N Dirichlet convolution of sigma and the Dirichlet inverse of A003961 (A346234).

%H Antti Karttunen, <a href="/A378607/b378607.txt">Table of n, a(n) for n = 1..20000</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences related to prime indices in the factorization of n</a>.

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

%F a(n) = Sum_{d|n} A000203(d)*A346234(n/d).

%F a(n) = Sum_{d|n} A349388(d).

%o (PARI)

%o A003961(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };

%o A346234(n) = (moebius(n)*A003961(n));

%o A378607(n) = sumdiv(n,d,sigma(d)*A346234(n/d));

%Y Cf. A000203, A003961, A016825, A346234, A378606 (Dirichlet inverse).

%Y Inverse Möbius transform of A349388.

%K sign,mult,new

%O 1,4

%A _Antti Karttunen_, Dec 11 2024