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

1,1

Comments

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

Links

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

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: A069976 A110546 A378054 * A335201 A267434 A048934

Adjacent sequences: A335137 A335138 A335139 * A335141 A335142 A335143

Keyword

nonn

Author

Amiram Eldar, May 25 2020

Status

approved