A357497 - OEIS

%I #9 Oct 03 2022 04:16:49

%S 4,9,12,18,24,25,28,45,49,54,60,90,112,121,126,132,150,153,168,169,

%T 198,270,289,294,336,361,364,414,529,560,594,630,637,684,726,841,918,

%U 961,1014,1140,1232,1305,1350,1369,1512,1521,1638,1680,1681,1710,1734,1849,1984

%N Nonsquarefree numbers whose harmonic mean of nonsquarefree divisors in an integer.

%C Analogous to harmonic numbers (A001599) with nonsquarefree divisors.

%C The squares of primes (A001248) are terms since they have a single nonsquarefree divisor.

%C If p is a prime then 6*p^2 is a term.

%H Amiram Eldar, <a href="/A357497/b357497.txt">Table of n, a(n) for n = 1..10000</a>

%e 12 is a term since its nonsquarefree divisors are 4 and 12 and their harmonic mean is 6 which is an integer.

%t q[n_] := Length[d = Select[Divisors[n], ! SquareFreeQ[#] &]] > 0 && IntegerQ[HarmonicMean[d]]; Select[Range[2000], q]

%Y Cf. A162296, A322609, A357493, A357494, A357495, A357496.

%Y Subsequence of A013929.

%Y Subsequence: A001248.

%Y Similar sequences: A001599 (harmonic numbers), A006086 (unitary), A063947 (infinitary), A286325 (bi-unitary), A319745 (nonunitary), A335387 (tri-unitary).

%K nonn

%O 1,1

%A _Amiram Eldar_, Oct 01 2022