A346236 Sum of A341530 and its Dirichlet inverse.

2, 0, 0, 1, 0, 4, 0, 1, 4, 4, 0, 70, 0, 8, 8, 9, 0, 134, 0, 2, 16, 4, 0, 52, 4, 4, -4, 44, 0, 368, 0, -3, 8, 4, 16, 1037, 0, 8, 8, 18, 0, 352, 0, 6, 460, 12, 0, 564, 16, -2, 8, 34, 0, -296, 8, 344, 16, 4, 0, 464, 0, 4, -8, 29, 8, 160, 0, 2, 24, 736, 0, -395, 0, 4, 460, 20, 16, 200, 0, -14, 21, 4, 0, 2152, 8, 8, 8, 740

Offset: 1

Author

Antti Karttunen, Jul 11 2021

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961, A341530, A346235.

Cf. also A346247, A346250, A346255.

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
A341530(n) = { my(t=A003961(n), s=sigma(t)); gcd((n*s), sigma(n)*t); };
v346235 = DirInverseCorrect(vector(up_to,n,A341530(n)));
A346235(n) = v346235[n];
A346236(n) = (A341530(n)+A346235(n));

Formula

a(n) = A341530(n) + A346235(n).