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