A292985 Bi-unitary pseudoperfect numbers: numbers that are equal to the sum of a subset of their aliquot bi-unitary divisors.

6, 24, 30, 40, 42, 48, 54, 56, 60, 66, 72, 78, 80, 88, 90, 96, 102, 104, 114, 120, 138, 150, 160, 162, 168, 174, 186, 192, 210, 216, 222, 224, 240, 246, 258, 264, 270, 280, 282, 288, 294, 312, 318, 320, 330, 336, 352, 354, 360, 366, 378, 384, 390, 402, 408

Offset

1,1

Comments

Analogous to pseudoperfect numbers (A005835) with bi-unitary sigma (A188999) instead of sigma (A000203).

Links

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

Example

48 is in the sequence since its bi-unitary divisors are 1, 2, 3, 6, 8, 16, 24, 48 and 48 = 8 + 16 + 24.

Mathematica

f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bdiv[m_] := Select[Divisors[m], Last@Intersection[f@#, f[m/#]] == 1 &]; a = {}; n = 0; While[n < 1000, n++; d = Most[bdiv[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 and Michael De Vlieger at A188999 *)

Crossrefs

Cf. A005835, A188999.

Sequence in context: A249667 A114274 A335215 * A335197 A364053 A306983

Adjacent sequences: A292982 A292983 A292984 * A292986 A292987 A292988

Keyword

nonn

Author

Amiram Eldar, Sep 27 2017

Status

approved