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 A348867 #11 Nov 02 2021 15:59:46 %S A348867 1,2,3,6,28,40,84,120,135,224,270,672,819,1638,3780,10880,13392,30240, %T A348867 32640,32760,167400,950976,1303533,2178540,2607066,3138345,4713984, %U A348867 6276690,8910720,14705145,17428320,29410290,45532800,52141320,179734464,301953024,311323824 %N A348867 Numbers whose numerator and denominator of the harmonic mean of their divisors are both 3-smooth numbers. %C A348867 The terms that are also harmonic numbers (A001599) are those whose harmonic mean of divisors (A001600) is a 3-smooth number. Of the 937 harmonic numbers below 10^14, 38 are terms in this sequence. %C A348867 If a term is not a harmonic number, then its numerator and denominator of the harmonic mean of its divisors are powers of 2 and 3, or vice versa. %C A348867 If k1 and k2 are coprime terms, then k1*k2 is also a term. In particular, if k is an odd term, then 2*k is also a term. %H A348867 Amiram Eldar, <a href="/A348867/b348867.txt">Table of n, a(n) for n = 1..47</a> %e A348867 2 is a term since the harmonic mean of its divisors is 4/3 = 2^2/3. %e A348867 3 is a term since the harmonic mean of its divisors is 3/2. %e A348867 40 is a term since the harmonic mean of its divisors is 32/9 = 2^5/3^2. %t A348867 smQ[n_] := n == 2^IntegerExponent[n, 2] * 3^IntegerExponent[n, 3]; h[n_] := DivisorSigma[0, n]/DivisorSigma[-1, n]; q[n_] := smQ[Numerator[(hn = h[n])]] && smQ[Denominator[hn]]; Select[Range[10^5], q] %Y A348867 Cf. A000079, A000244, A001599, A001600, A003586, A099377, A099378. %Y A348867 Subsequence of A348868. %Y A348867 Similar sequences: A074266, A122254, A348658, A348659. %K A348867 nonn %O A348867 1,2 %A A348867 _Amiram Eldar_, Nov 02 2021