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A267310 a(n) is the numerator of Sum_{d|n} sigma(n/d)^d/d, where sigma is A000203. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 30 17:12 EST 2021. Contains 349424 sequences. (Running on oeis4.)