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 A361384 #13 Mar 10 2023 10:53:47 %S A361384 0,2,2,3,3,4,4,3,4,5,4,5,4,3,4,5,4,5,4,4,3,5,4,5,5,5,5,5,5,4,5,5,4,5, %T A361384 5,5,5,4,4,4,5,6,5,6,5,5,6,6,5,5,6,6,5,5,6,6,6,6,5,6,5,6,6,6,5,6,5,6, %U A361384 5,6,5,6,4,5,6,6,6,6,5,6,5,6,6,6,6,5,6 %N A361384 a(n) is the number of distinct prime factors of the n-th unitary harmonic number. %C A361384 Each term appears a finite number of times in the sequence (Hagis and Lord, 1975). %H A361384 Amiram Eldar, <a href="/A361384/b361384.txt">Table of n, a(n) for n = 1..290</a> %H A361384 Peter Hagis, Jr. and Graham Lord, <a href="https://doi.org/10.1090/S0002-9939-1975-0369231-9">Unitary harmonic numbers</a>, Proc. Amer. Math. Soc., Vol. 51, No. 1 (1975), pp. 1-7. %F A361384 a(n) = A001221(A006086(n)). %t A361384 uh[n_] := n * Times @@ (2/(1 + Power @@@ FactorInteger[n])); uh[1] = 1; PrimeNu[Select[Range[10^6], IntegerQ[uh[#]] &]] %o A361384 (PARI) uhmean(n) = {my(f = factor(n)); n*prod(i=1, #f~, 2/(1+f[i, 1]^f[i, 2])); }; %o A361384 lista(kmax) = {my(uh); for(k = 1, kmax, uh = uhmean(k); if(denominator(uh) == 1, print1(omega(k), ", ")));} %Y A361384 Cf. A001221, A006086, A006087. %K A361384 nonn %O A361384 1,2 %A A361384 _Amiram Eldar_, Mar 10 2023