A379580 Denominators of the partial sums of the reciprocals of the powerfree part function (A055231).
1, 2, 6, 6, 30, 5, 35, 35, 35, 70, 770, 2310, 30030, 15015, 5005, 5005, 85085, 170170, 3233230, 3233230, 9699690, 4849845, 111546435, 111546435, 111546435, 223092870, 223092870, 223092870, 6469693230, 1078282205, 33426748355, 33426748355, 9116385915, 18232771830
Offset: 1
References
- 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.
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 4.11, pp. 31-32.
Programs
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Mathematica
f[p_, e_] := If[e==1, p, 1]; powfree[n_] := Times @@ f @@@ FactorInteger[n]; Denominator[Accumulate[Table[1/powfree[n], {n, 1, 50}]]] -
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 / powfree(k); print1(denominator(s), ", "))};
Formula
a(n) = denominator(Sum_{k=1..n} 1/A055231(k)).