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 A349178 #11 Jan 14 2023 16:14:04
%S A349178 1645,5742,6336,8925,9450,88473
%N A349178 Nonexponential harmonic numbers: numbers k that are not prime powers such that the harmonic mean of the nonexponential divisors of k is an integer.
%C A349178 The prime powers are excluded since the primes and the squares of primes have a single nonexponential divisor (the number 1).
%C A349178 a(7) > 6.6*10^10, if it exists.
%e A349178 1645 is a term since the set of its nonexponential divisors is {1, 5, 7, 35, 47, 235, 329} and the harmonic mean of this set, 5, is an integer.
%t A349178 dQ[n_, m_] := (n > 0 && m > 0 && Divisible[n, m]); expDivQ[n_, d_] := Module[{ft = FactorInteger[n]}, And @@ MapThread[dQ, {ft[[;; , 2]], IntegerExponent[d, ft[[;; , 1]]]}]]; neDivs[1] = {0}; neDivs[n_] := Module[{d = Divisors[n]}, Select[d, ! expDivQ[n, #] &]]; Select[Range[10^4], Length[(d = neDivs[#])] > 1 && IntegerQ @ HarmonicMean[d] &]
%Y A349178 Cf. A160097, A160135.
%Y A349178 Similar sequences: A001599, A006086, A063947, A286325, A319745, A348964, A349026.
%K A349178 nonn,more
%O A349178 1,1
%A A349178 _Amiram Eldar_, Nov 09 2021