A378752 a(n) = 2*sigma(n) - sigma(A003961(n)), where A003961 is fully multiplicative with a(prime(i)) = prime(i+1).

1, 2, 2, 1, 4, 0, 4, -10, -5, 4, 10, -22, 10, 0, 0, -59, 16, -46, 16, -20, -8, 16, 18, -120, 5, 12, -76, -44, 28, -48, 26, -238, 12, 28, 0, -221, 34, 24, 4, -140, 40, -96, 40, -14, -92, 24, 42, -478, -19, -42, 24, -38, 48, -384, 32, -240, 16, 52, 58, -288, 56, 40, -164, -839, 24, -48, 64, -8, 12, -96, 70, -850, 68, 60

Offset: 1

Author

Antti Karttunen, Dec 09 2024

Keywords

• sign

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 A000203, A003961, A003973.

Cf. A337381 (positions of terms <= 0), A337382 (of terms > 0), A337384 (positions of 0's),

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A378752(n) = ((2*sigma(n)) - sigma(A003961(n)));

Formula

a(n) = 2*A000203(n) - A003973(n).