A268982 a(n) is the denominator of Sum_{d|n} sigma(n/d)^d/d, where sigma is A000203.

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, 28, 29, 6, 31, 32, 33, 34, 35, 18, 37, 38, 1, 40, 41, 6, 43, 44, 9, 46, 47, 16, 49, 25, 51, 52, 53, 27, 55, 56, 19, 58, 59, 60, 61, 62, 21, 64, 65, 66, 67, 68, 69

Offset

1,2

Comments

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

a(n) is a divisor of n. How often is it < n? - Chai Wah Wu, Oct 02 2017

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Example

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.

Maple

a := proc (n) options operator, arrow; add(numtheory:-sigma(n/d)^d/d, d in numtheory:-divisors(n)) end proc:
seq(denom(a(n)), n = 1 .. 100);

Mathematica

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

Prog

(PARI) a(n) = denominator(sumdiv(n, d, sigma(n/d)^d/d)); \\ Michel Marcus, Feb 17 2016
(Python)
from __future__ import division
from sympy import divisors, divisor_sigma, gcd
def A268982(n):
    return n//gcd(n, sum(d*divisor_sigma(d)**(n//d)  for d in divisors(n, generator=True))) # Chai Wah Wu, Oct 02 2017

Crossrefs

Cf. A000203, A267310, A268983.

Sequence in context: A053834 A297245 A043273 * A278065 A373233 A291041

Adjacent sequences: A268979 A268980 A268981 * A268983 A268984 A268985

Keyword

nonn,frac

Author

Gevorg Hmayakyan, Feb 16 2016

Status

approved