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

1,1

Comments

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.

Links

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

Example

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

Mathematica

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

Crossrefs

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).

Sequence in context: A312863 A312864 A326071 * A319745 A312865 A376340

Adjacent sequences: A357494 A357495 A357496 * A357498 A357499 A357500

Keyword

nonn

Author

Amiram Eldar, Oct 01 2022

Status

approved