A346248 Dirichlet inverse of -A252748, 2*n - A003961(n).

1, -1, -1, 2, -3, 5, -3, 8, 8, 7, -9, 10, -9, 11, 11, 32, -15, 16, -15, 6, 19, 13, -17, 48, 8, 17, 56, 18, -27, -3, -25, 128, 17, 19, 25, 104, -33, 23, 25, 32, -39, 9, -39, -6, 24, 29, -41, 224, 32, 16, 23, 6, -47, 144, 35, 88, 31, 31, -57, 78, -55, 37, 72, 512, 43, -33, -63, -18, 41, -13, -69, 512, -67, 41, 40, -6, 43

Offset: 1

Author

Antti Karttunen, Jul 19 2021

Keywords

• sign
• look

Comments

Zeros occur at n = 352, 26840, 34816, 3787168, ...

Links

• Antti Karttunen, Table of n, a(n) for n = 1..34816
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A003961, A252748, A346250.

Cf. also A323910, A346235, A346246, A346254.

Programs

PARI

up_to = 16384;
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
v346248 = DirInverseCorrect(vector(up_to,n,(n+n)-A003961(n)));
A346248(n) = v346248[n];

Formula

a(n) = A346250(n) + A252748(n).