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

Author

Asher Auel, Jan 19 2000

Keywords

• nonn
• easy

Comments

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

Examples

			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).
		

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.

Crossrefs

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

Programs

Haskell

a054024 n = mod (a000203 n) n  -- Reinhard Zumkeller, Mar 23 2013

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 *)

PARI

a(n)=sigma(n)%n \\ Charles R Greathouse IV, Nov 04 2014

Formula

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

a(p) = 1 for p prime.