VOOZH about

URL: https://oeis.org/A379582

⇱ A379582 - OEIS

login
A379582
Denominators of the partial alternating sums of the reciprocals of the powerfree part function (A055231).
3
1, 2, 6, 6, 30, 15, 105, 105, 105, 210, 2310, 2310, 30030, 15015, 1001, 1001, 17017, 34034, 646646, 3233230, 9699690, 4849845, 111546435, 37182145, 37182145, 74364290, 74364290, 74364290, 2156564410, 3234846615, 100280245065, 100280245065, 100280245065, 200560490130
OFFSET
1,2
LINKS
László Tóth, Alternating Sums Concerning Multiplicative Arithmetic Functions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.11, pp. 31-32.
FORMULA
a(n) = denominator(Sum_{k=1..n} (-1)^(k+1)/A055231(k)).
MATHEMATICA
f[p_, e_] := If[e==1, p, 1]; powfree[n_] := Times @@ f @@@ FactorInteger[n]; Denominator[Accumulate[Table[(-1)^(n+1)/powfree[n], {n, 1, 50}]]]
PROG
(PARI) powfree(n) = {my(f = factor(n)); prod(i=1, #f~, if(f[i, 2] == 1, f[i, 1], 1)); }
list(nmax) = {my(s = 0); for(k = 1, nmax, s += (-1)^(k+1) / powfree(k); print1(denominator(s), ", "))};
CROSSREFS
Cf. A055231, A370900, A370901, A379580, A379581 (numerators).
Sequence in context: A333072 A333196 A216850 * A070889 A072744 A374317
KEYWORD
nonn,easy,frac
AUTHOR
Amiram Eldar, Dec 26 2024
STATUS
approved