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

1,1

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, ...

Links

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

Example

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.

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]

Crossrefs

Subsequence of A293188 and A334405.

A002827 is a subsequence.

Cf. A077610.

Sequence in context: A185288 A189000 A007358 * A322486 A323757 A376889

Adjacent sequences: A334403 A334404 A334405 * A334407 A334408 A334409

Keyword

nonn

Author

Amiram Eldar, Apr 27 2020

Status

approved