A379584 Denominators of the partial sums of the reciprocals of the powerful part function (A057521).

1, 1, 1, 4, 4, 4, 4, 8, 72, 72, 72, 72, 72, 72, 72, 144, 144, 144, 144, 144, 144, 144, 144, 144, 3600, 3600, 10800, 10800, 10800, 10800, 10800, 21600, 21600, 21600, 21600, 21600, 21600, 21600, 21600, 21600, 21600, 21600, 21600, 21600, 21600, 21600, 21600, 21600, 1058400

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Maurice-Étienne Cloutier, Les parties k-puissante et k-libre d'un nombre, Thèse de doctorat, Université Laval, Québec (2018).

Maurice-Étienne Cloutier, Jean-Marie De Koninck, and Nicolas Doyon, On the powerful and squarefree parts of an integer, Journal of Integer Sequences, Vol. 17 (2014), Article 14.6.6.

László Tóth, Alternating Sums Concerning Multiplicative Arithmetic Functions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.12, p. 33.

Formula

a(n) = denominator(Sum_{k=1..n} 1/A057521(k)).

Mathematica

f[p_, e_] := If[e > 1, p^e, 1]; powful[n_] := Times @@ f @@@ FactorInteger[n]; Denominator[Accumulate[Table[1/powful[n], {n, 1, 50}]]]

Prog

(PARI) powerful(n) = {my(f = factor(n)); prod(i=1, #f~, if(f[i, 2] > 1, f[i, 1]^f[i, 2], 1)); }
list(nmax) = {my(s = 0); for(k = 1, nmax, s += 1 / powerful(k); print1(denominator(s), ", "))};

Crossrefs

Cf. A057521, A370902, A370903, A379583 (numerators), A379586.

Sequence in context: A114555 A361471 A379586 * A124570 A213083 A053187

Adjacent sequences: A379581 A379582 A379583 * A379585 A379586 A379587

Keyword

nonn,easy,frac,new

Author

Amiram Eldar, Dec 26 2024

Status

approved