A268983 Numbers n such that Sum_{d|n} sigma(n/d)^d/d is an integer, where sigma is A000203.

1, 39, 793, 25930965, 76147347

Offset

1,2

Comments

Conjecture: This sequence contains only the three numbers listed.

This conjecture is disproven. The number 2408321608150261253061174553 belongs to this sequence, but it may not be a(4). - Gevorg Hmayakyan, May 11 2017

a(6) > 10^8. - Hiroaki Yamanouchi, Aug 10 2017

Numbers n such that n divides Sum_{d|n} d*sigma(d)^(n/d). - Chai Wah Wu, Oct 02 2017

Links

Table of n, a(n) for n=1..5.

The integer values of Sum_{d|n} sigma(n/d)^d/d

Maple

a := proc (n) options operator, arrow; add(numtheory:-sigma(n/d)^d/d, d in numtheory:-divisors(n)) end proc:
seq(`if`(type(a(n), 'integer'), n, NULL), n = 1 .. 1000)

Mathematica

Select[Range[10^5], IntegerQ@ Sum[DivisorSigma[1, #/d]^d/d, {d, Divisors@ #}] &] (* Michael De Vlieger, Mar 30 2016 *)

Prog

(PARI) isok(n) = denominator(sumdiv(n, d, sigma(n/d)^d/d)) == 1; \\ Michel Marcus, Feb 17 2016
(Python)
from __future__ import division
from sympy import divisors, divisor_sigma
A268983_list = [n for n in range(1, 10000) if not sum(d*pow(int(divisor_sigma(d)), n//d, n) % n for d in divisors(n, generator=True)) % n] # Chai Wah Wu, Oct 02 2017

Crossrefs

Cf. A000203, A267310, A268982.

Sequence in context: A232354 A232067 A247222 * A293918 A264458 A004330

Adjacent sequences: A268980 A268981 A268982 * A268984 A268985 A268986

Keyword

nonn,more

Author

Gevorg Hmayakyan, Feb 16 2016

Extensions

a(4)-a(5) from Hiroaki Yamanouchi, Aug 10 2017

Status

approved