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A348868 Numbers whose numerator and denominator of the harmonic mean of their divisors are both 5-smooth numbers.

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%I A348868 #11 Nov 02 2021 15:59:53
%S A348868 1,2,3,5,6,8,10,15,24,27,28,30,40,54,84,120,135,140,216,224,270,420,
%T A348868 496,672,756,775,819,1080,1120,1488,1550,1638,2176,2325,2480,3360,
%U A348868 3780,4095,4650,6048,6200,6528,6552,7440,8190,10880,11375,13392,18600,20925,21700
%N A348868 Numbers whose numerator and denominator of the harmonic mean of their divisors are both 5-smooth numbers.
%C A348868 The terms that are also harmonic numbers (A001599) are those whose harmonic mean of divisors (A001600) is a 5-smooth number. Of the 937 harmonic numbers below 10^14, 83 are terms in this sequence.
%C A348868 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 A348868 Amiram Eldar, <a href="/A348868/b348868.txt">Table of n, a(n) for n = 1..234</a>
%e A348868 8 is a term since the harmonic mean of its divisors is 32/15 and both 32 = 2^5 and 15 = 3*5 are 5-smooth numbers.
%t A348868 smQ[n_] := n == 2^IntegerExponent[n, 2] * 3^IntegerExponent[n, 3] * 5^IntegerExponent[n, 5]; h[n_] := DivisorSigma[0, n]/DivisorSigma[-1, n]; q[n_] := smQ[Numerator[(hn = h[n])]] && smQ[Denominator[hn]]; Select[Range[22000], q]
%Y A348868 Cf. A001599, A001600, A051037, A099377, A099378.
%Y A348868 A348867 is a subsequence.
%Y A348868 Similar sequences: A074266, A348658, A348659.
%K A348868 nonn
%O A348868 1,2
%A A348868 _Amiram Eldar_, Nov 02 2021