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

Author

Amiram Eldar, Apr 15 2025

Keywords

• nonn
• easy
• frac

Examples

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

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.

Crossrefs

The unitary analog of A104529.

Cf. A034444, A383055 (numerators).

Similar sequences: A064608, A370898, A379514.

Programs

Mathematica

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

PARI

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

Formula

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