A267310 a(n) is the numerator of Sum_{d|n} sigma(n/d)^d/d, where sigma is A000203.

1, 7, 13, 47, 31, 175, 57, 479, 310, 847, 133, 4799, 183, 737, 4513, 25023, 307, 32123, 381, 195887, 17803, 356671, 553, 1892351, 39656, 3192287, 807286, 12898415, 871, 6727787, 993, 109575039, 12603505, 258287671, 1630737, 502527043, 1407, 2324532815

Offset

1,2

Comments

If n is prime, a(n) = n^2 + n + 1. - Robert Israel, Feb 16 2016

Links

Chai Wah Wu, Table of n, a(n) for n = 1..4191

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) = numerator(175/6) = 175.

Maple

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

Mathematica

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

Prog

(PARI) a(n) = numerator(sumdiv(n, d, sigma(n/d)^d/d)); \\ Michel Marcus, Feb 19 2016
(Python)
from __future__ import division
from sympy import divisors, divisor_sigma, gcd
def A267310(n):
    m = sum(d*divisor_sigma(d)**(n//d)  for d in divisors(n, generator=True))
    return m//gcd(m, n) # Chai Wah Wu, Oct 02 2017

Crossrefs

Cf. A000203, A268982, A268983.

Sequence in context: A159305 A146648 A219501 * A153119 A166703 A116522

Adjacent sequences: A267307 A267308 A267309 * A267311 A267312 A267313

Keyword

nonn,frac

Author

Gevorg Hmayakyan, Feb 16 2016

Status

approved