login
A319296
a(n) = (Sum_{d|n} (sigma(d))) mod sigma(n).
4
0, 1, 1, 4, 1, 8, 1, 11, 5, 10, 1, 27, 1, 12, 11, 26, 1, 33, 1, 35, 13, 16, 1, 10, 7, 18, 18, 43, 1, 68, 1, 57, 17, 22, 15, 16, 1, 24, 19, 2, 1, 84, 1, 59, 48, 28, 1, 37, 9, 59, 23, 67, 1, 112, 19, 114, 25, 34, 1, 49, 1, 36, 58, 120, 21, 116, 1, 83, 29, 108
OFFSET
1,4
COMMENTS
a(n) = A007429(n) mod A000203(n).
LINKS
FORMULA
a(A221219(n)) = 0.
a(A000040(n)) = 1; the only composite number < 2*10^6 with a(n) = 1 is 636.
a(n) = n only for numbers 4, 10 and 96 < 3000000.
EXAMPLE
For n = 4; a(4) = ((sigma(1) + sigma(2) + sigma(4)) mod sigma(4) = (1+3+7) mod 7 = 11 mod 7 = 4.
MATHEMATICA
Table[Mod[Sum[DivisorSigma[1, d], {d, Divisors[n]}], DivisorSigma[1, n]], {n, 1, 100}] (* Vaclav Kotesovec, Sep 26 2018 *)
PROG
(Magma) [&+[SumOfDivisors(d): d in Divisors(n)] mod SumOfDivisors(n): n in [1..1000]]
(PARI) A319296(n) = (sumdiv(n, d, sigma(d))%sigma(n)); \\ Antti Karttunen, Sep 16 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Sep 16 2018
STATUS
approved