A293188 Unitary pseudoperfect numbers: numbers that equal to the sum of a subset of their aliquot unitary divisors.

6, 30, 42, 60, 66, 78, 90, 102, 114, 138, 150, 174, 186, 210, 222, 246, 258, 282, 294, 318, 330, 354, 366, 390, 402, 420, 426, 438, 462, 474, 498, 510, 534, 546, 570, 582, 606, 618, 630, 642, 654, 660, 678, 690, 714, 726, 750, 762, 770, 780, 786, 798, 822

Offset: 1

Author

Amiram Eldar, Oct 01 2017

Keywords

• nonn

Comments

Supersequence of A002827.

The nonsquarefree terms are 60, 90, 150, 294, 420, 630, 660, 726, 750, 780, 840, ...

Examples

			150 is in the sequence since its unitary aliquot divisors are 1, 2, 3, 6, 25, 50, 75 and 150 = 25 + 50 + 75.
		

Links

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

Crossrefs

Cf. A002827, A005835, A034683, A064114.

Programs

Mathematica

udiv[n_]:=Block[{d=Divisors[n]},Select[d,GCD[#,n/#]==1&]]; a={};n=0;While[Length[a]<100,n++;d=Most[udiv[n]];c = SeriesCoefficient[ Series[ Product[1+x^d[[i]],{i,Length[d]} ],{x,0,n}], n]; If[c>0,AppendTo[a,n]]];a (* after T. D. Noe at A005835 *)