

A357846


Denominators of the partial alternating sums of the reciprocals of the sum of divisors function (A000203).


2



1, 3, 12, 84, 84, 7, 56, 840, 10920, 32760, 32760, 32760, 32760, 16380, 32760, 1015560, 338520, 338520, 338520, 338520, 1354080, 4062240, 4062240, 4062240, 131040, 131040, 131040, 131040, 131040, 43680, 21840, 65520, 32760, 98280, 196560, 196560, 3734640, 3734640
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OFFSET

1,2


COMMENTS



LINKS



FORMULA

a(n) = denominator(Sum_{k=1..n} (1)^(k+1)/sigma(k)), where sigma(k) = A000203(k).


MATHEMATICA

Denominator[Accumulate[Array[(1)^(# + 1)/DivisorSigma[1, #] &, 60]]]


PROG

(PARI) lista(nmax) = {my(s = 0); for(k = 1, nmax, s += (1)^(k+1) / sigma(k); print1(denominator(s), ", "))};
(Python)
from fractions import Fraction
from sympy import divisor_sigma
def A357846(n): return sum(Fraction(1 if k&1 else 1, divisor_sigma(k)) for k in range(1, n+1)).denominator # Chai Wah Wu, Oct 16 2022


CROSSREFS



KEYWORD

nonn,frac


AUTHOR



STATUS

approved



