A379364 Denominators of the partial sums of the reciprocals of Pillai's arithmetical function (A018804).

1, 3, 15, 120, 360, 360, 4680, 4680, 32760, 98280, 98280, 12285, 61425, 61425, 61425, 982800, 10810800, 1544400, 57142800, 57142800, 57142800, 399999600, 399999600, 79999920, 1230768, 30769200, 92307600, 1199998800, 22799977200, 22799977200, 1390798609200, 695399304600

Offset

1,2

Links

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

László Tóth, A survey of gcd-sum functions, Journal of Integer Sequences, Vol. 13 (2010), Article 10.8.1. See pp. 18-19.

László Tóth, Alternating Sums Concerning Multiplicative Arithmetic Functions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.5, pp. 23-24.

Shiqin Chen and Wenguang Zhai, Reciprocals of the Gcd-Sum Functions, Journal of Integer Sequences, Vol. 14 (2011), Article 11.8.3.

Formula

a(n) = denominator(Sum_{k=1..n} 1/A018804(k)).

Mathematica

f[p_, e_] := (e*(p-1)/p + 1)*p^e; pillai[n_] := Times @@ f @@@ FactorInteger[n]; Denominator[Accumulate[Table[1/pillai[n], {n, 1, 50}]]]

Prog

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

Crossrefs

Cf. A018804, A272718, A370895, A379363 (numerators), A379366.

Sequence in context: A060639 A068052 A379366 * A068859 A006454 A225115

Adjacent sequences: A379361 A379362 A379363 * A379365 A379366 A379367

Keyword

nonn,easy,frac

Author

Amiram Eldar, Dec 21 2024

Status

approved