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%I #31 Oct 03 2017 02:14:34
%S 1,7,13,47,31,175,57,479,310,847,133,4799,183,737,4513,25023,307,
%T 32123,381,195887,17803,356671,553,1892351,39656,3192287,807286,
%U 12898415,871,6727787,993,109575039,12603505,258287671,1630737,502527043,1407,2324532815
%N a(n) is the numerator of Sum_{d|n} sigma(n/d)^d/d, where sigma is A000203.
%C If n is prime, a(n) = n^2 + n + 1. - _Robert Israel_, Feb 16 2016
%H Chai Wah Wu, <a href="/A267310/b267310.txt">Table of n, a(n) for n = 1..4191</a>
%e sigma(1)^6/6 + sigma(2)^3/3 + sigma(3)^2/2 + sigma(6)^1/1 = 1/6 + 9 + 8 + 12 = 175/6. a(6) = numerator(175/6) = 175.
%p a := proc (n) options operator, arrow; add(numtheory:-sigma(n/d)^d/d, d in numtheory:-divisors(n)) end proc:
%p seq(numer(a(n)), n = 1 .. 100);
%t Table[Numerator@ Sum[DivisorSigma[1, n/d]^d/d, {d, Divisors@ n}], {n,
%t 38}] (* _Michael De Vlieger_, Feb 19 2016 *)
%o (PARI) a(n) = numerator(sumdiv(n, d, sigma(n/d)^d/d)); \\ _Michel Marcus_, Feb 19 2016
%o (Python)
%o from __future__ import division
%o from sympy import divisors, divisor_sigma, gcd
%o def A267310(n):
%o m = sum(d*divisor_sigma(d)**(n//d) for d in divisors(n, generator=True))
%o return m//gcd(m,n) # _Chai Wah Wu_, Oct 02 2017
%Y Cf. A000203, A268982, A268983.
%K nonn,frac
%O 1,2
%A _Gevorg Hmayakyan_, Feb 16 2016
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