A378755 Dirichlet convolution of A033879 and A346248.

1, 0, 1, 2, 1, 2, 3, 10, 11, 2, 1, 14, 3, 6, 7, 42, 1, 26, 3, 14, 17, 2, 5, 70, 15, 6, 81, 34, 1, 22, 5, 170, 7, 2, 17, 146, 3, 6, 17, 70, 1, 54, 3, 14, 69, 10, 5, 326, 55, 34, 7, 34, 5, 234, 7, 162, 17, 2, 1, 138, 5, 10, 155, 682, 17, 22, 3, 14, 27, 54, 1, 730, 5, 6, 89, 34, 17, 54, 3, 326, 571, 2, 5, 318, 7, 6, 7

Offset: 1

Author

Antti Karttunen, Dec 11 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to prime indices in the factorization of n.
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A033879, A346248, A378754 (Dirichlet inverse).

Programs

PARI

A033879(n) = (n+n-sigma(n));
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A252748(n) = (A003961(n) - (2*n));
memoA346248 = Map();
A346248(n) = if(1==n,1,my(v); if(mapisdefined(memoA346248,n,&v), v, v = -sumdiv(n,d,if(dA252748(n/d)*A346248(d),0)); mapput(memoA346248,n,v); (v)));
A378755(n) = sumdiv(n,d,A033879(d)*A346248(n/d));

Formula

a(n) = Sum_{d|n} A033879(d)*A346248(n/d).