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A054024 Sum of divisors of n reduced modulo n. 38
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Walter Nissen, Abundancy : Some Resources

FORMULA

a(n) = A000203(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, A007691, A045768, A045769, A088834, A045770, A076496, A159907.

Sequence in context: A055807 A213060 A272008 * A144644 A151509 A264434

Adjacent sequences:  A054021 A054022 A054023 * A054025 A054026 A054027

KEYWORD

nonn,easy

AUTHOR

Asher Auel (asher.auel(AT)reed.edu) Jan 19, 2000

STATUS

approved

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Last modified December 3 01:12 EST 2016. Contains 278694 sequences.