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 A348866 #17 Nov 02 2021 15:59:40 %S A348866 6,15,20,28,33,35,42,51,66,69,70,84,87,114,117,123,135,138,140,141, %T A348866 153,159,177,186,204,207,210,213,249,258,267,270,273,276,282,285,297, %U A348866 303,308,321,339,348,354,357,372,393,399,402,411,420,426,432,435,447,464 %N A348866 Composite numbers k such that A099378(k) | (A099377(k) + 1). %C A348866 A disjoint union of the harmonic numbers (A001599) and the composite numbers whose harmonic mean of divisors is of the form m - 1/k, where m and k are integers. %C A348866 If p is an odd prime, then the harmonic mean of its divisors is p*tau(p)/sigma(p) = p*A000005(p)/A000203(p) = p/((p+1)/2), so A099378(p) | (A099377(p) + 1). Therefore, this sequence is restricted to composite numbers. %C A348866 This sequence is infinite. For example, it includes all the semiprimes of the form 3*p, where p == 2 (mod 3). %H A348866 Amiram Eldar, <a href="/A348866/b348866.txt">Table of n, a(n) for n = 1..10000</a> %e A348866 15 is a term since it is composite, the harmonic mean of divisors of 15 is 5/2 and 2 | (5+1). %t A348866 h[n_] := DivisorSigma[0, n]/DivisorSigma[-1, n]; q[n_] := Divisible[Numerator[(h1 = h[n])] + 1, Denominator[h1]]; Select[Range[1000], CompositeQ[#] && q[#] &] %Y A348866 Cf. A000005, A000203, A001599, A003627, A099377, A099378, A348865. %K A348866 nonn %O A348866 1,1 %A A348866 _Amiram Eldar_, Nov 02 2021