The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A357555 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A357555

a(n) is the numerator of Sum_{d|n} (-1)^(d+1) / d^2.
(history; published version)

#10 by Michael De Vlieger at Sat Oct 08 15:11:12 EDT 2022

STATUS

reviewed

approved

#9 by Hugo Pfoertner at Sat Oct 08 14:27:43 EDT 2022

STATUS

proposed

reviewed

#8 by Michel Marcus at Mon Oct 03 09:48:50 EDT 2022

STATUS

editing

proposed

#7 by Michel Marcus at Mon Oct 03 09:48:45 EDT 2022

PROG

(PARI) a(n) = numerator(sumdiv(n, d, (-1)^(d+1)/d^2)); \\ Michel Marcus, Oct 03 2022

STATUS

proposed

editing

#6 by Michael S. Branicky at Mon Oct 03 09:25:05 EDT 2022

STATUS

editing

proposed

#5 by Michael S. Branicky at Mon Oct 03 09:25:02 EDT 2022

PROG

(Python)

from sympy import divisors

from fractions import Fraction

def a(n): return sum(Fraction((-1)**(d+1), d*d) for d in divisors(n, generator=True)).numerator

print([a(n) for n in range(1, 56)]) # Michael S. Branicky, Oct 03 2022

STATUS

proposed

editing

#4 by Ilya Gutkovskiy at Mon Oct 03 06:49:36 EDT 2022

STATUS

editing

proposed

#3 by Ilya Gutkovskiy at Mon Oct 03 06:22:25 EDT 2022

CROSSREFS

Cf. A017667, A064027, A098987, A119682, A321543, A357556 (denominators).

#2 by Ilya Gutkovskiy at Mon Oct 03 06:17:34 EDT 2022

NAME

allocated for Ilya Gutkovskiya(n) is the numerator of Sum_{d|n} (-1)^(d+1) / d^2.

DATA

1, 3, 10, 11, 26, 5, 50, 43, 91, 39, 122, 55, 170, 75, 52, 171, 290, 91, 362, 143, 500, 183, 530, 215, 651, 255, 820, 275, 842, 13, 962, 683, 1220, 435, 52, 1001, 1370, 543, 1700, 559, 1682, 125, 1850, 61, 2366, 795, 2210, 95, 2451, 1953, 2900, 935, 2810, 205, 3172

OFFSET

1,2

FORMULA

Numerators of coefficients in expansion of Sum_{k>=1} (-1)^(k+1) * x^k / (k^2 * (1 - x^k)).

EXAMPLE

1, 3/4, 10/9, 11/16, 26/25, 5/6, 50/49, 43/64, 91/81, 39/50, 122/121, ...

MATHEMATICA

Table[Sum[(-1)^(d + 1)/d^2, {d, Divisors[n]}], {n, 1, 55}] // Numerator

nmax = 55; CoefficientList[Series[Sum[(-1)^(k + 1) x^k/(k^2 (1 - x^k)), {k, 1, nmax}], {x, 0, nmax}], x] // Numerator // Rest

CROSSREFS

Cf. A017667, A064027, A098987, A119682, A321543

KEYWORD

allocated

nonn,frac

AUTHOR

Ilya Gutkovskiy, Oct 03 2022

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Mon Oct 03 06:17:34 EDT 2022

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved