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 A379579 #7 Dec 26 2024 20:02:19
%S A379579 1,3,11,17,91,16,117,152,187,381,4261,13553,178499,90322,30441,35446,
%T A379579 607587,1300259,24875091,25521737,77027101,38733998,895731799,
%U A379579 932913944,1044460379,2097501253,2320594123,2352464533,68444564327,11443370128,355822756173,389249504528
%N A379579 Numerators of the partial sums of the reciprocals of the powerfree part function (A055231).
%D A379579 D. Suryanarayana and P. Subrahmanyam, The maximal k-full divisor of an integer, Indian J. Pure Appl. Math., Vol. 12, No. 2 (1981), pp. 175-190.
%H A379579 Amiram Eldar, <a href="/A379579/b379579.txt">Table of n, a(n) for n = 1..1000</a>
%H A379579 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 A379579 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 A379579 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 4.11, pp. 31-32.
%F A379579 a(n) = numerator(Sum_{k=1..n} 1/A055231(k)).
%F A379579 a(n)/A379580(n) = A * n^(1/2) + B * n^(1/3) + O(n^(1/5)), where A = A328013, and B = (zeta(2/3)/zeta(2)) * Product_{p prime} (1 + (p^(1/3)-1)/(p*(p^(2/3)-p^(1/3)+1))) = -2.59305556147555965163... .
%e A379579 Fractions begin with 1, 3/2, 11/6, 17/6, 91/30, 16/5, 117/35, 152/35, 187/35, 381/70, 4261/770, 13553/2310, ...
%t A379579 f[p_, e_] := If[e==1, p, 1]; powfree[n_] := Times @@ f @@@ FactorInteger[n]; Numerator[Accumulate[Table[1/powfree[n], {n, 1, 50}]]]
%o A379579 (PARI) powfree(n) = {my(f = factor(n)); prod(i=1, #f~, if(f[i, 2] == 1, f[i, 1], 1)); }
%o A379579 list(nmax) = {my(s = 0); for(k = 1, nmax, s += 1 / powfree(k); print1(numerator(s), ", "))};
%Y A379579 Cf. A055231, A328013, A370900, A370901, A379580 (denominators), A379581.
%K A379579 nonn,easy,frac
%O A379579 1,2
%A A379579 _Amiram Eldar_, Dec 26 2024