A374903 Denominator of the mean number of divisors of the divisors of n.

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

Offset

1,2

Links

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

Formula

a(A374904(n)) = 1.

a(A374905(n)) = 1.

Example

For n = 2, n has 2 divisors, 1 and 2. Their numbers of divisors are tau(1) = 1 and tau(2) = 2, and their mean number of divisors is (1 + 2)/2 = 3/2. Therefore a(2) = denominator(3/2) = 2.

Mathematica

f[p_, e_] := (e + 2)/2; a[1] = 1; a[n_] := Denominator[Times @@ f @@@ FactorInteger[n]]; Array[a, 100]

Prog

(PARI) a(n) = denominator(vecprod(apply(x -> x/2 +1, factor(n)[, 2])));

Crossrefs

Cf. A374902 (numerators), A374904, A374905.

Sequence in context: A380086 A278763 A278762 * A055076 A069780 A369307

Adjacent sequences: A374900 A374901 A374902 * A374904 A374905 A374906

Keyword

nonn,easy,frac

Author

Amiram Eldar, Jul 23 2024

Status

approved