

A335140


Unitary pseudoperfect numbers (A293188) that are nonsquarefree.


2



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
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OFFSET

1,1


COMMENTS

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


LINKS

Table of n, a(n) for n=1..46.


EXAMPLE

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.


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]


CROSSREFS

Intersection of A013929 and A293188.
Subsequence of A005835.
Sequence in context: A100659 A069976 A110546 * A335201 A267434 A048934
Adjacent sequences: A335136 A335137 A335138 * A335141 A335142 A335143


KEYWORD

nonn


AUTHOR

Amiram Eldar, May 25 2020


STATUS

approved



