A361318 - OEIS

%I #10 Mar 10 2023 10:39:18

%S 1,2,3,4,4,6,7,7,11,13,13,10,7,15,16,15,9,20,18,14,25,24,19,25,15,27,

%T 28,30,18,36,13,21,17,29,40,33,24,28,38,31,29,45,34,27,28,44,27,60,36,

%U 52,46,26,51,42,55,33,66,40,24,37,49,29,47,57,34,68,49,44

%N Harmonic means of the infinitary divisors of the infinitary harmonic numbers.

%C Each term appears a finite number of times in the sequence (Hagis and Cohen, 1990).

%H Amiram Eldar, <a href="/A361318/b361318.txt">Table of n, a(n) for n = 1..239</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) = A361316(A063947(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}]]; s[1] = 1; s[n_] := n * Times @@ f @@@ FactorInteger[n]; Select[Array[s, 10^4], IntegerQ]

%o (PARI) ihmean(n) = {my(f = factor(n), b); 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))); };

%o lista(kmax) = {my(ih); for(k = 1, kmax, ih = ihmean(k); if(denominator(ih) == 1, print1(ih, ", ")));}

%Y Cf. A063947, A361316, A361317.

%Y Similar sequences: A001600, A006087.

%K nonn

%O 1,2

%A _Amiram Eldar_, Mar 09 2023