A378751 a(n) = A000203(n) - A048673(n).

0, 1, 1, 2, 2, 4, 2, 1, 0, 7, 5, 5, 5, 7, 6, -10, 8, 1, 8, 10, 4, 16, 9, -8, 6, 16, -23, 6, 14, 19, 13, -59, 15, 25, 9, -22, 17, 25, 13, -5, 20, 13, 20, 25, -10, 28, 21, -79, -4, 19, 24, 21, 24, -68, 26, -29, 22, 43, 29, 10, 28, 40, -34, -238, 24, 46, 32, 40, 23, 28, 35, -143, 34, 52, 1, 36, 24, 40, 38, -98, -192

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, A048673, A377984, A378747.

Cf. A337378 (positions of negative terms), A337379 (of terms >= 0).

Programs

PARI

A048673(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); (factorback(f)+1)/2; };
A378751(n) = (sigma(n)-A048673(n));

Formula

a(n) = n - A378747(n).

a(n) = (1/2) * (A377984(n)-1).