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

1,4

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).

Formula

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

Prog

(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(d<n, -A252748(n/d)*A346248(d), 0)); mapput(memoA346248, n, v); (v)));
A378755(n) = sumdiv(n, d, A033879(d)*A346248(n/d));

Crossrefs

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

Sequence in context: A034952 A378754 A337549 * A306456 A178463 A213593

Adjacent sequences: A378752 A378753 A378754 * A378763 A378767 A378768

Keyword

nonn,new

Author

Antti Karttunen, Dec 11 2024

Status

approved