

A292985


Biunitary pseudoperfect numbers: numbers that are equal to the sum of a subset of their aliquot biunitary divisors.


7



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
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OFFSET

1,1


COMMENTS

Analogous to pseudoperfect numbers (A005835) with biunitary sigma (A188999) instead of sigma (A000203).


LINKS

Table of n, a(n) for n=1..55.


EXAMPLE

48 is in the sequence since its biunitary 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 A306983 A234648
Adjacent sequences: A292982 A292983 A292984 * A292986 A292987 A292988


KEYWORD

nonn


AUTHOR

Amiram Eldar, Sep 27 2017


STATUS

approved



