A361317 - OEIS

%I #9 Mar 10 2023 10:37:35

%S 1,3,2,5,3,1,4,15,5,9,6,5,7,3,2,17,9,5,10,3,8,9,12,5,13,21,10,5,15,3,

%T 16,51,4,27,12,25,19,15,14,9,21,2,22,15,1,9,24,17,25,39,6,35,27,5,18,

%U 15,20,45,30,1,31,12,20,85,21,3,34,45,8,9,36,25,37,57

%N Denominators of the harmonic means of the infinitary divisors of the positive integers.

%H Amiram Eldar, <a href="/A361317/b361317.txt">Table of n, a(n) for n = 1..10000</a>

%H Peter Hagis, Jr. and Graeme L. Cohen, <a href="http://dx.doi.org/10.1017/S0004972700017949">Infinitary harmonic numbers</a>, Bull. Australian Math. Soc., Vol. 41, No. 1 (1990), pp. 151-158.

%F a(n) = denominator(n*A037445(n)/A049417(n)).

%t f[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 2/(1 + p^(2^(m - j))), 1], {j, 1, m}]]; a[1] = 1; a[n_] := Denominator[n * Times @@ f @@@ FactorInteger[n]]; Array[a, 100]

%o (PARI) a(n) = {my(f = factor(n), b); denominator(n * prod(i=1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], 2/(f[i, 1]^(2^(#b-k))+1), 1)))); }

%Y Cf. A037445, A049417, A077609, A063947 (positions of 1's), A361316 (numerators).

%Y Similar sequences: A099378, A103340.

%K nonn,frac

%O 1,2

%A _Amiram Eldar_, Mar 09 2023