

A054024


Sum of divisors of n reduced modulo n.


36



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
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OFFSET

1,4


COMMENTS

If a(n) = 0, then n is a multiplyperfect 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 A205099 * A144644 A151509 A151511
Adjacent sequences: A054021 A054022 A054023 * A054025 A054026 A054027


KEYWORD

nonn,easy


AUTHOR

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


STATUS

approved



