A334406 Unitary pseudoperfect numbers k such that there is a subset of unitary divisors of k whose sum is 2*k and for each d in this subset k/d is also in it.

6, 60, 90, 210, 330, 546, 660, 714, 1770, 2310, 2730, 3198, 3486, 3570, 3990, 4290, 4620, 4830, 5460, 5610, 6006, 6090, 6270, 6510, 6630, 6930, 7140, 7410, 7590, 7770, 7854, 7980, 8190, 8580, 8610, 8778, 8970, 9030, 9240, 9570, 9660, 9690, 9870, 10374, 10626, 10710

Offset: 1

Author

Amiram Eldar, Apr 27 2020

Keywords

• nonn

Comments

Includes all the unitary perfect numbers (A002827).

The squarefree terms of A334405 are also terms of this sequence. Terms that are not squarefree are 60, 90, 660, 4620, 5460, 6930, 7140, 7980, 8190, 8580, 9240, 9660, ...

Examples

			210 is a term since {1, 2, 3, 14, 15, 70, 105, 210} is a subset of its unitary divisors whose sum is 420 = 2 * 210, and for each divisor d in this subset 210/d is also in it: 1 * 210 = 2 * 105 = 3 * 70 = 14 * 15 = 210.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..450

Crossrefs

Subsequence of A293188 and A334405.

A002827 is a subsequence.

Cf. A077610.

Programs

Mathematica

seqQ[n_] := Module[{d = Select[Divisors[n], CoprimeQ[#, n/#] &]}, nd = Length[d]; divpairs = d[[1 ;; nd/2]] + d[[-1 ;; nd/2 + 1 ;; -1]]; SeriesCoefficient[Series[Product[1 + x^divpairs[[i]], {i, Length[divpairs]}], {x, 0, 2*n}], 2*n] > 0]; Select[Range[2, 1000], seqQ]