A318996 a(n) = Sum_{d|n} (sigma(n) mod d).

0, 1, 1, 4, 1, 0, 1, 11, 5, 11, 1, 9, 1, 13, 13, 26, 1, 10, 1, 8, 17, 17, 1, 16, 7, 19, 18, 0, 1, 28, 1, 57, 19, 23, 22, 34, 1, 25, 23, 24, 1, 41, 1, 65, 45, 29, 1, 57, 9, 68, 25, 75, 1, 39, 25, 25, 29, 35, 1, 88, 1, 37, 74, 120, 29, 37, 1, 91, 31, 24, 1, 103

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Carlos Rivera, Puzzle 1065. A larger integer than 45 such that ..., The Prime Puzzles and Problems Connection.

Formula

a(A007691(n)) = 0.

a(A000040(n)) = 1.

a(A008578(n)) = tau(n) - 1.

a(n) = n for numbers 4, 45, 6048, 14421, ...

Example

For n = 4; a(4) = (7 mod 1) + (7 mod 2) + (7 mod 4) = 0 + 1 + 3 = 4.

Mathematica

a[n_] := Block[{s = DivisorSigma[1, n]}, DivisorSum[n, Mod[s, #] &]]; Array[a, 72] (* Giovanni Resta, Sep 07 2018 *)

Prog

(Magma) [&+[SumOfDivisors(n) mod d: d in Divisors(n)] : n in [1..1000]]
(PARI) a(n) = my(sn = sigma(n)); sumdiv(n, d, sn % d); \\ Michel Marcus, Sep 07 2018
(Python)
from sympy import divisors
def a(n): divs = divisors(n); s = sum(divs); return sum(s%d for d in divs)
print([a(n) for n in range(1, 73)]) # Michael S. Branicky, Nov 27 2021

Crossrefs

Cf. A000005, A000040, A000203, A007691, A008578, A300657.

Sequence in context: A294118 A343648 A359363 * A294490 A085852 A123125

Adjacent sequences: A318993 A318994 A318995 * A318997 A318998 A318999

Keyword

nonn

Author

Jaroslav Krizek, Sep 07 2018

Status

approved