A346010 a(n) is the denominator of the average number of distinct prime factors of the divisors of n.

1, 2, 2, 3, 2, 1, 2, 4, 3, 1, 2, 6, 2, 1, 1, 5, 2, 6, 2, 6, 1, 1, 2, 4, 3, 1, 4, 6, 2, 2, 2, 6, 1, 1, 1, 3, 2, 1, 1, 4, 2, 2, 2, 6, 6, 1, 2, 10, 3, 6, 1, 6, 2, 4, 1, 4, 1, 1, 2, 3, 2, 1, 6, 7, 1, 2, 2, 6, 1, 2, 2, 12, 2, 1, 6, 6, 1, 2, 2, 10, 5, 1, 2, 3, 1, 1

Offset

1,2

Comments

See A346009 for details.

Links

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

R. L. Duncan, Note on the divisors of a number, The American Mathematical Monthly, Vol. 68, No. 4 (1961), pp. 356-359.

Sébastien Gaboury, Sur les convolutions de fonctions arithmétiques, M.Sc. thesis, Laval University, Quebec, 2007.

Mathematica

a[n_] := Denominator[DivisorSum[n, PrimeNu[#] &]/DivisorSigma[0, n]]; Array[a, 100]
(* or *)
f[p_, e_] := e/(e+1); a[1] = 1; a[n_] := Denominator[Plus @@ f @@@ FactorInteger[n]]; Array[a, 100]

Crossrefs

Cf. A346009 (numerators).

Sequence in context: A007906 A044050 A096826 * A116199 A369031 A162915

Adjacent sequences: A346007 A346008 A346009 * A346011 A346012 A346013

Keyword

nonn,frac

Author

Amiram Eldar, Jul 01 2021

Status

approved