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
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.
Programs
-
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}]]] -
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), ", "))};
Formula
a(n) = denominator(Sum_{k=1..n} 1/A018804(k)).