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A054024 Sum of the divisors of n reduced modulo n. 44
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
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).
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
KEYWORD
nonn,easy
AUTHOR
Asher Auel, Jan 19 2000
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)