A374903 - OEIS

%I #8 Jul 23 2024 20:46:40

%S 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,

%T 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,

%U 4,8,2,1,2,4,1,1,4,8,2,2,1,4,2,2,4,4,4

%N Denominator of the mean number of divisors of the divisors of n.

%H Amiram Eldar, <a href="/A374903/b374903.txt">Table of n, a(n) for n = 1..10000</a>

%F a(A374904(n)) = 1.

%F a(A374905(n)) = 1.

%e 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.

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

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

%Y Cf. A374902 (numerators), A374904, A374905.

%K nonn,easy,frac

%O 1,2

%A _Amiram Eldar_, Jul 23 2024