A383056 Denominators of the partial sums of the reciprocals of the number of unitary divisors function (A034444).

1, 2, 1, 2, 1, 4, 4, 4, 4, 1, 2, 4, 4, 2, 4, 4, 4, 1, 2, 4, 1, 4, 4, 1, 2, 4, 4, 2, 1, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 1, 2, 4, 1, 4, 4, 1, 2, 4, 1, 4, 4, 1, 4, 2, 4, 1, 2, 8, 8, 8, 8, 8, 8, 2, 1, 4, 2, 8, 8, 8, 8, 8, 8, 8, 8, 1, 2, 4, 4, 2, 1, 8, 8, 8, 8, 8

Offset

1,2

References

Jean-Marie De Koninck and Aleksandar Ivić, Topics in Arithmetical Functions, North-Holland Publishing Company, Amsterdam, Netherlands, 1980. See pp. 42-43.

Steven R. Finch, Mathematical Constants II, Cambridge University Press, 2018, p. 50.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Jean-Marie De Koninck and Jacques Grah, Arithmetic functions and weighted averages, Colloquium Mathematicum, Vol. 79. No. 2 (1999), pp. 249-272.

Formula

a(n) = denominator(Sum_{k=1..n} 1/A034444(k)).

Example

Fractions begin with 1, 3/2, 2, 5/2, 3, 13/4, 15/4, 17/4, 19/4, 5, 11/2, 23/4, ...

Mathematica

Denominator[Accumulate[1/Array[2^PrimeNu[#] &, 100]]]

Prog

(PARI) list(nmax) = {my(s = 0); for(k = 1, nmax, s += 1 / 2^omega(k); print1(denominator(s), ", "))};

Crossrefs

The unitary analog of A104529.

Cf. A034444, A383055 (numerators).

Similar sequences: A064608, A370898, A379514.

Sequence in context: A216327 A380480 A099875 * A079499 A166235 A143591

Adjacent sequences: A383053 A383054 A383055 * A383057 A383058 A383059

Keyword

nonn,easy,frac

Author

Amiram Eldar, Apr 15 2025

Status

approved