cp's OEIS Frontend

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.

%I A334406 #12 Apr 28 2020 05:56:38
%S A334406 6,60,90,210,330,546,660,714,1770,2310,2730,3198,3486,3570,3990,4290,
%T A334406 4620,4830,5460,5610,6006,6090,6270,6510,6630,6930,7140,7410,7590,
%U A334406 7770,7854,7980,8190,8580,8610,8778,8970,9030,9240,9570,9660,9690,9870,10374,10626,10710
%N 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.
%C A334406 Includes all the unitary perfect numbers (A002827).
%C A334406 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, ...
%H A334406 Amiram Eldar, <a href="/A334406/b334406.txt">Table of n, a(n) for n = 1..450</a>
%e A334406 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.
%t A334406 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]
%Y A334406 Subsequence of A293188 and A334405.
%Y A334406 A002827 is a subsequence.
%Y A334406 Cf. A077610.
%K A334406 nonn
%O A334406 1,1
%A A334406 _Amiram Eldar_, Apr 27 2020