A295829 Unitary pseudoperfect numbers that equal to the sum of a subset of their aliquot unitary divisors in a single way.

6, 60, 78, 90, 102, 114, 138, 150, 174, 186, 222, 246, 258, 282, 294, 318, 354, 366, 402, 426, 438, 474, 498, 534, 582, 606, 618, 642, 654, 678, 726, 750, 762, 786, 822, 834, 894, 906, 942, 978, 1002, 1014, 1038, 1074, 1086, 1146, 1158, 1182, 1194, 1266, 1338

Offset: 1

Author

Amiram Eldar, Nov 28 2017

Keywords

• nonn

Comments

The unitary version of A064771.

It appears that most of the terms are divisible by 3. Terms that are not divisible by 3 are 3770, 5530, 7210, 7630, ... - Michel Marcus, Dec 15 2017

The least odd term is 442365. - Amiram Eldar, Jun 10 2020

Examples

			150 is in the sequence since its aliquot unitary divisors are 1, 2, 3, 6, 25, 50, 75 and there is only one subset whose sum is 150: {25, 50, 75}.
		

Links

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

Crossrefs

Cf. A064771, A293188.

Programs

Mathematica

ud[n_] := Block[{d = Divisors[n]}, Select[d, GCD[#, n/#] == 1 &]];
a = {}; n = 0; While[Length[a] < 100, n++; d = Most[ud[n]];
c = SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n]; If[c ==1, AppendTo[a, n]]]; a