A335387 -id:A335387 - cp's OEIS frontend

A357497 Nonsquarefree numbers whose harmonic mean of nonsquarefree divisors in an integer.

4, 9, 12, 18, 24, 25, 28, 45, 49, 54, 60, 90, 112, 121, 126, 132, 150, 153, 168, 169, 198, 270, 289, 294, 336, 361, 364, 414, 529, 560, 594, 630, 637, 684, 726, 841, 918, 961, 1014, 1140, 1232, 1305, 1350, 1369, 1512, 1521, 1638, 1680, 1681, 1710, 1734, 1849, 1984

Offset: 1

Amiram Eldar, Oct 01 2022

nonn

Analogous to harmonic numbers (A001599) with nonsquarefree divisors.
The squares of primes (A001248) are terms since they have a single nonsquarefree divisor.
If p is a prime then 6*p^2 is a term.

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A162296, A322609, A357493, A357494, A357495, A357496.
Subsequence of A013929.
Subsequence: A001248.
Similar sequences: A001599 (harmonic numbers), A006086 (unitary), A063947 (infinitary), A286325 (bi-unitary), A319745 (nonunitary), A335387 (tri-unitary).

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

cp's OEIS Frontend

A357497 Nonsquarefree numbers whose harmonic mean of nonsquarefree divisors in an integer.

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