A377984 a(n) = 2*sigma(n) - A003961(n), where sigma is the sum of divisors function and A003961 is fully multiplicative function with a(prime(i)) = prime(i+1).

1, 3, 3, 5, 5, 9, 5, 3, 1, 15, 11, 11, 11, 15, 13, -19, 17, 3, 17, 21, 9, 33, 19, -15, 13, 33, -45, 13, 29, 39, 27, -117, 31, 51, 19, -43, 35, 51, 27, -9, 41, 27, 41, 51, -19, 57, 43, -157, -7, 39, 49, 43, 49, -135, 53, -57, 45, 87, 59, 21, 57, 81, -67, -475, 49, 93, 65, 81, 47, 57, 71, -285, 69, 105, 3, 73, 49, 81

Offset: 1

Author

Antti Karttunen, Nov 16 2024

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A003961.

Cf. A337378 (positions of negative terms), A337379 (of positive terms), A337380 (their characteristic function), A377985 (Möbius transform).

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A377984(n) = (2*sigma(n) - A003961(n));