A379520 Denominators of the partial alternating sums of the reciprocals of the unitary totient function (A047994).

1, 1, 2, 6, 12, 12, 12, 84, 168, 168, 840, 840, 280, 840, 105, 105, 1680, 1680, 5040, 5040, 5040, 5040, 55440, 55440, 55440, 55440, 720720, 80080, 80080, 80080, 240240, 7447440, 7447440, 3723720, 620620, 3723720, 11171160, 11171160, 1396395, 5585580, 2234232, 2234232

Offset

1,3

Links

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

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.

Formula

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

Mathematica

uphi[n_] := Times @@ (-1 + Power @@@ FactorInteger[n]); uphi[1] = 1; Denominator[Accumulate[Table[(-1)^(n+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)^(k+1) / uphi(k); print1(denominator(s), ", "))};

Crossrefs

Cf. A047994, A177754, A370899, A379518, A379519 (numerators).

Sequence in context: A074385 A057340 A092427 * A058198 A096075 A278256

Adjacent sequences: A379517 A379518 A379519 * A379521 A379522 A379525

Keyword

nonn,easy,frac,new

Author

Amiram Eldar, Dec 24 2024

Status

approved