A227758 - OEIS

A227758

a(n) = sigma(sigma(n)) - sigma(n) - n, where sigma(n) = A000203(n) = sum of the divisors of n.

-1, -1, 0, -3, 1, 10, 0, 1, -8, 11, 5, 16, -3, 22, 21, -15, 4, -1, 3, 34, 10, 33, 13, 84, -24, 28, 23, 36, 13, 93, 0, 9, 43, 32, 41, -15, -15, 70, 25, 104, 13, 114, -3, 96, 45, 77, 29, 52, -26, -15, 72, 21, 13, 186, 68, 184, 49, 86, 49, 252, -27, 94, 43, -63

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

Conjecture: a(n) = 0 for Mersenne primes (A000668). [This is easily proved: For Mersenne primes n=2^p-1, sigma(n)=n+1=2^p, sigma(2^p)=2^(p+1)-1, thus a(n)=0. - M. F. Hasler, Jul 30 2013]

a(n) < 0 for numbers n from A227759, a(n) > 0 for numbers n from A227760.

Sequence contains anomalous increased frequency of values 13 (see A227756).

LINKS

Paul Tek, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A051027(n) - A000203(n) - n.

EXAMPLE

For n = 6; a(n) = sigma(sigma(6)) - sigma(6) - 6 = 28 - 12 - 6 = 10.

PROG

(PARI) a(n) = my(s=sigma(n)); sigma(s)-s-n; \\ Michel Marcus, Sep 10 2025

CROSSREFS

Cf. A051027, A000203, A000668, A227759, A227760, A227756.