A379363 Numerators of the partial sums of the reciprocals of Pillai's arithmetical function (A018804).
1, 4, 23, 199, 637, 661, 8953, 9187, 65869, 201247, 205927, 26048, 132697, 134272, 135637, 2190667, 24424937, 3513791, 131554667, 132348317, 133227437, 938941259, 947830139, 190366027, 2947643, 74101331, 223443593, 2916305159, 55809797621, 55978686341, 3437499844001
Offset: 1
Examples
Fractions begin with 1, 4/3, 23/15, 199/120, 637/360, 661/360, 8953/4680, 9187/4680, 65869/32760, 201247/98280, 205927/98280, 26048/12285, ...
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]; Numerator[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(numerator(s), ", "))};