A323894 Sum of A048673 and its Dirichlet inverse, A323893.

2, 0, 0, 4, 0, 12, 0, 12, 9, 16, 0, 26, 0, 24, 24, 37, 0, 46, 0, 36, 36, 28, 0, 76, 16, 36, 51, 56, 0, 58, 0, 114, 42, 40, 48, 121, 0, 48, 54, 106, 0, 94, 0, 66, 104, 60, 0, 223, 36, 92, 60, 86, 0, 220, 56, 166, 72, 64, 0, 164, 0, 76, 162, 349, 72, 112, 0, 96, 90, 136, 0, 354, 0, 84, 150, 116, 84, 148, 0, 312, 277, 88, 0, 260, 80, 96, 96

Offset: 1

Author

Antti Karttunen, Feb 08 2019

Keywords

• sign

Comments

The first four negative terms are a(3063060) = -14126242, a(3423420) = -17546656, a(4084080) = -14460312, a(4144140) = -22677277. - Antti Karttunen, Apr 20 2022

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16383
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to prime indices in the factorization of n.

Crossrefs

Cf. A003961, A048673, A323893, A349135.

Cf. also A323365, A323412, A323896, A349135, A349349, A353336.

Programs

PARI

up_to = 65537;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA003961(n) = my(f = factor(n)); for (i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); \\ From A003961
A048673(n) = (A003961(n)+1)/2;
v323893 = DirInverse(vector(up_to,n,A048673(n)));
A323893(n) = v323893[n];
A323894(n) = (A048673(n)+A323893(n));

Formula

a(n) = A048673(n) + A323893(n).

For n > 1, a(n) = -Sum_{d|n, 1A048673(n/d) * A323893(d). - Antti Karttunen, Apr 20 2022

a(n) = A349135(A003961(n)). - Antti Karttunen, Nov 30 2024