A379518 Denominators of the partial sums of the reciprocals of the unitary totient function (A047994).

1, 1, 2, 6, 12, 12, 4, 28, 56, 56, 280, 840, 280, 840, 210, 42, 336, 336, 1008, 1008, 1008, 5040, 55440, 55440, 55440, 55440, 720720, 720720, 102960, 102960, 102960, 3191760, 3191760, 199485, 1595880, 797940, 199485, 398970, 1595880, 11171160, 1117116, 279279

Offset

1,3

Links

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

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018. See p. 52.

V. Sita Ramaiah and D. Suryanarayana, Sums of reciprocals of some multiplicative functions - II, Indian J. Pure Appl. Math., Vol. 11 (1980), pp. 1334-1355.

László Tóth, Alternating Sums Concerning Multiplicative Arithmetic Functions, Journal of Integer Sequences, Vol. 20 (2017), Article 17.2.1. See section 4.10, pp. 30-31.

Rimer Zurita, Generalized Alternating Sums of Multiplicative Arithmetic Functions, Journal of Integer Sequences, Vol. 23 (2020), Article 20.10.4. See section 4.5, pp. 16-17.

Formula

a(n) = denominator(Sum_{k=1..n} 1/A047994(k)).

Mathematica

uphi[n_] := Times @@ (-1 + Power @@@ FactorInteger[n]); uphi[1] = 1; Denominator[Accumulate[Table[1/uphi[n], {n, 1, 50}]]]

Prog

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

Crossrefs

Cf. A047994, A177754, A370899, A379517 (numerators), A379520.

Sequence in context: A069491 A127698 A379620 * A130503 A278232 A074385

Adjacent sequences: A379515 A379516 A379517 * A379519 A379520 A379521

Keyword

nonn,easy,frac

Author

Amiram Eldar, Dec 24 2024

Status

approved