This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A361318 #10 Mar 10 2023 10:39:18 %S A361318 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 A361318 28,30,18,36,13,21,17,29,40,33,24,28,38,31,29,45,34,27,28,44,27,60,36, %U A361318 52,46,26,51,42,55,33,66,40,24,37,49,29,47,57,34,68,49,44 %N A361318 Harmonic means of the infinitary divisors of the infinitary harmonic numbers. %C A361318 Each term appears a finite number of times in the sequence (Hagis and Cohen, 1990). %H A361318 Amiram Eldar, <a href="/A361318/b361318.txt">Table of n, a(n) for n = 1..239</a> %H A361318 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 A361318 a(n) = A361316(A063947(n)). %t A361318 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 A361318 (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 A361318 lista(kmax) = {my(ih); for(k = 1, kmax, ih = ihmean(k); if(denominator(ih) == 1, print1(ih, ", ")));} %Y A361318 Cf. A063947, A361316, A361317. %Y A361318 Similar sequences: A001600, A006087. %K A361318 nonn %O A361318 1,2 %A A361318 _Amiram Eldar_, Mar 09 2023