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

1,2

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.

Formula

a(n) = denominator(Sum_{k=1..n} 1/A055231(k)).

Mathematica

f[p_, e_] := If[e==1, p, 1]; powfree[n_] := Times @@ f @@@ FactorInteger[n]; Denominator[Accumulate[Table[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 / powfree(k); print1(denominator(s), ", "))};

Crossrefs

Cf. A055231, A370900, A370901, A379579 (numerators), A379582.

Sequence in context: A130087 A085087 A072983 * A055204 A212397 A008339

Adjacent sequences: A379577 A379578 A379579 * A379581 A379582 A379583

Keyword

nonn,easy,frac

Author

Amiram Eldar, Dec 26 2024

Status

approved