A335140 Unitary pseudoperfect numbers (A293188) that are nonsquarefree.

60, 90, 150, 294, 420, 630, 660, 726, 750, 780, 840, 924, 990, 1014, 1020, 1050, 1092, 1140, 1170, 1380, 1386, 1428, 1470, 1530, 1596, 1638, 1650, 1710, 1734, 1740, 1860, 1890, 1950, 2058, 2070, 2142, 2166, 2220, 2394, 2460, 2550, 2580, 2610, 2790, 2820, 2850

Offset: 1

Author

Amiram Eldar, May 25 2020

Keywords

• nonn

Comments

The pseudoperfect numbers (A005835) that are squarefree are also unitary pseudoperfect numbers (A293188) since all of their divisors are unitary.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A013929 and A293188.

Subsequence of A005835.

Programs

Mathematica

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]