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

Author

Amiram Eldar, Sep 27 2017

Keywords

• nonn

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A005835, A188999.

Programs

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 *)