This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A379584 #6 Dec 26 2024 20:03:05
%S A379584 1,1,1,4,4,4,4,8,72,72,72,72,72,72,72,144,144,144,144,144,144,144,144,
%T A379584 144,3600,3600,10800,10800,10800,10800,10800,21600,21600,21600,21600,
%U A379584 21600,21600,21600,21600,21600,21600,21600,21600,21600,21600,21600,21600,21600,1058400
%N A379584 Denominators of the partial sums of the reciprocals of the powerful part function (A057521).
%H A379584 Amiram Eldar, <a href="/A379584/b379584.txt">Table of n, a(n) for n = 1..1000</a>
%H A379584 Maurice-Étienne Cloutier, <a href="http://hdl.handle.net/20.500.11794/28374">Les parties k-puissante et k-libre d'un nombre</a>, Thèse de doctorat, Université Laval, Québec (2018).
%H A379584 Maurice-Étienne Cloutier, Jean-Marie De Koninck, and Nicolas Doyon, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL17/Cloutier/cloutier2.html">On the powerful and squarefree parts of an integer</a>, Journal of Integer Sequences, Vol. 17 (2014), Article 14.6.6.
%H A379584 László Tóth, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL20/Toth/toth25.html">Alternating Sums Concerning Multiplicative Arithmetic Functions</a>, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.12, p. 33.
%F A379584 a(n) = denominator(Sum_{k=1..n} 1/A057521(k)).
%t A379584 f[p_, e_] := If[e > 1, p^e, 1]; powful[n_] := Times @@ f @@@ FactorInteger[n]; Denominator[Accumulate[Table[1/powful[n], {n, 1, 50}]]]
%o A379584 (PARI) powerful(n) = {my(f = factor(n)); prod(i=1, #f~, if(f[i, 2] > 1, f[i, 1]^f[i, 2], 1)); }
%o A379584 list(nmax) = {my(s = 0); for(k = 1, nmax, s += 1 / powerful(k); print1(denominator(s), ", "))};
%Y A379584 Cf. A057521, A370902, A370903, A379583 (numerators), A379586.
%K A379584 nonn,easy,frac
%O A379584 1,4
%A A379584 _Amiram Eldar_, Dec 26 2024