A268982 - OEIS

%I #34 Oct 03 2017 06:23:45

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,2,15,16,17,9,19,20,7,22,23,24,25,26,27,

%T 28,29,6,31,32,33,34,35,18,37,38,1,40,41,6,43,44,9,46,47,16,49,25,51,

%U 52,53,27,55,56,19,58,59,60,61,62,21,64,65,66,67,68,69

%N a(n) is the denominator of Sum_{d|n} sigma(n/d)^d/d, where sigma is A000203.

%C If n is prime, a(n) = n.

%C a(n) is a divisor of n. How often is it < n? - _Chai Wah Wu_, Oct 02 2017

%H Chai Wah Wu, <a href="/A268982/b268982.txt">Table of n, a(n) for n = 1..10000</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) = denominator(175/6) = 6.

%p a := proc (n) options operator, arrow; add(numtheory:-sigma(n/d)^d/d, d in numtheory:-divisors(n)) end proc:

%p seq(denom(a(n)), n = 1 .. 100);

%t Table[Denominator@ Sum[DivisorSigma[1, n/d]^d/d, {d, Divisors@ n}], {n, 69}] (* _Michael De Vlieger_, Feb 19 2016 *)

%o (PARI) a(n) = denominator(sumdiv(n, d, sigma(n/d)^d/d)); \\ _Michel Marcus_, Feb 17 2016

%o (Python)

%o from __future__ import division

%o from sympy import divisors, divisor_sigma, gcd

%o def A268982(n):

%o     return n//gcd(n,sum(d*divisor_sigma(d)**(n//d)  for d in divisors(n, generator=True))) # _Chai Wah Wu_, Oct 02 2017

%Y Cf. A000203, A267310, A268983.

%K nonn,frac

%O 1,2

%A _Gevorg Hmayakyan_, Feb 16 2016