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%I #12 Apr 04 2023 07:43:30
%S 60,90,150,294,420,630,660,726,750,780,840,924,990,1014,1020,1050,
%T 1092,1140,1170,1380,1386,1428,1470,1530,1596,1638,1650,1710,1734,
%U 1740,1860,1890,1950,2058,2070,2142,2166,2220,2394,2460,2550,2580,2610,2790,2820,2850
%N Unitary pseudoperfect numbers (A293188) that are nonsquarefree.
%C The pseudoperfect numbers (A005835) that are squarefree are also unitary pseudoperfect numbers (A293188) since all of their divisors are unitary.
%H Amiram Eldar, <a href="/A335140/b335140.txt">Table of n, a(n) for n = 1..10000</a>
%e 60 is a term since it is nonsquarefree (it is divisible by 4 = 2^2) and it is equal to a sum of its aliquot unitary divisors: 1 + 3 + 4 + 5 + 12 + 15 + 20 = 60.
%t pspQ[n_] := !SquareFreeQ[n] && Module[{d = Most @ Select[Divisors[n], CoprimeQ[#, n/#] &], x}, Plus @@ d >= n && SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] > 0]; Select[Range[1000], pspQ]
%Y Intersection of A013929 and A293188.
%Y Subsequence of A005835.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 25 2020