%I #45 Oct 03 2017 02:52:24
%S 1,39,793,25930965,76147347
%N Numbers n such that Sum_{d|n} sigma(n/d)^d/d is an integer, where sigma is A000203.
%C Conjecture: This sequence contains only the three numbers listed.
%C This conjecture is disproven. The number 2408321608150261253061174553 belongs to this sequence, but it may not be a(4). - _Gevorg Hmayakyan_, May 11 2017
%C a(6) > 10^8. - _Hiroaki Yamanouchi_, Aug 10 2017
%C Numbers n such that n divides Sum_{d|n} d*sigma(d)^(n/d). - _Chai Wah Wu_, Oct 02 2017
%H <a href="https://math.stackexchange.com/questions/2272764/the-integer-values-of-sum-dn-frac-sigman-ddd">The integer values of Sum_{d|n} sigma(n/d)^d/d</a>
%p a := proc (n) options operator, arrow; add(numtheory:-sigma(n/d)^d/d, d in numtheory:-divisors(n)) end proc:
%p seq(`if`(type(a(n), 'integer'), n, NULL), n = 1 .. 1000)
%t Select[Range[10^5], IntegerQ@ Sum[DivisorSigma[1, #/d]^d/d, {d, Divisors@ #}] &] (* _Michael De Vlieger_, Mar 30 2016 *)
%o (PARI) isok(n) = denominator(sumdiv(n, d, sigma(n/d)^d/d)) == 1; \\ _Michel Marcus_, Feb 17 2016
%o (Python)
%o from __future__ import division
%o from sympy import divisors, divisor_sigma
%o 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
%Y Cf. A000203, A267310, A268982.
%K nonn,more
%O 1,2
%A _Gevorg Hmayakyan_, Feb 16 2016
%E a(4)-a(5) from _Hiroaki Yamanouchi_, Aug 10 2017