A374127 a(n) = (sigma(n) - sopfr(n)) - n, where sigma is the sum of divisors, and sopfr is the sum of prime factors (with repetition).

0, -1, -2, -1, -4, 1, -6, 1, -2, 1, -10, 9, -12, 1, 1, 7, -16, 13, -18, 13, 1, 1, -22, 27, -4, 1, 4, 17, -28, 32, -30, 21, 1, 1, 1, 45, -36, 1, 1, 39, -40, 42, -42, 25, 22, 1, -46, 65, -6, 31, 1, 29, -52, 55, 1, 51, 1, 1, -58, 96, -60, 1, 28, 51, 1, 62, -66, 37, 1, 60, -70, 111, -72, 1, 36, 41, 1, 72, -78, 93, 28

Offset: 1

Author

Antti Karttunen, Jul 06 2024

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A000203, A001414, A075254, A086665, A374128, A374129.

Programs

PARI

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]);
A374127(n) = ((sigma(n)-A001414(n))-n);

Formula

a(n) = A086665(n) - n.

a(n) = A000203(n) - A075254(n);