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

1,1

Comments

Supersequence of A002827.

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A002827, A005835, A034683, A064114.

Sequence in context: A101937 A101939 A290466 * A080289 A175907 A114649

Adjacent sequences: A293185 A293186 A293187 * A293189 A293190 A293191

Keyword

nonn

Author

Amiram Eldar, Oct 01 2017

Status

approved