A054024 Sum of the divisors of n reduced modulo n.

0, 1, 1, 3, 1, 0, 1, 7, 4, 8, 1, 4, 1, 10, 9, 15, 1, 3, 1, 2, 11, 14, 1, 12, 6, 16, 13, 0, 1, 12, 1, 31, 15, 20, 13, 19, 1, 22, 17, 10, 1, 12, 1, 40, 33, 26, 1, 28, 8, 43, 21, 46, 1, 12, 17, 8, 23, 32, 1, 48, 1, 34, 41, 63, 19, 12, 1, 58, 27, 4, 1, 51, 1, 40, 49, 64, 19, 12, 1, 26, 40

Offset

1,4

Comments

If a(n) = 0, then n is a multiply-perfect number (A007691). - Alonso del Arte, Mar 30 2014

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537 (first 1000 terms from T. D. Noe, terms 1001..20000 from Alois P. Heinz).

Walter Nissen, Abundancy : Some Resources.

Formula

a(n) = sigma(n) mod n.

a(p) = 1 for p prime.

Example

a(12) = 4 because sigma(12) = 28 and 28 == 4 (mod 12).
a(13) = 1 because 13 is prime.
a(14) = 10 because sigma(14) = 24 and 24 == 10 (mod 14).

Maple

with(numtheory): seq(sigma(i) mod i, i=1..100);

Mathematica

Table[Mod[DivisorSigma[1, n], n], {n, 80}] (* Alonso del Arte, Mar 30 2014 *)

Prog

(Haskell)
a054024 n = mod (a000203 n) n  -- Reinhard Zumkeller, Mar 23 2013
(PARI) a(n)=sigma(n)%n \\ Charles R Greathouse IV, Nov 04 2014

Crossrefs

Cf. A000203 (sigma), A005114 (untouchable numbers), A007691 (positions of 0's), A045768, A045769, A088834, A045770, A076496, A159907.

Sequence in context: A364285 A213060 A272008 * A144644 A151509 A264434

Adjacent sequences: A054021 A054022 A054023 * A054025 A054026 A054027

Keyword

nonn,easy

Author

Asher Auel, Jan 19 2000

Status

approved