

A335938


Biunitary pseudoperfect numbers (A292985) that are not exponentially odd numbers (A268335).


2



48, 60, 72, 80, 90, 150, 162, 192, 240, 288, 294, 320, 336, 360, 420, 432, 448, 504, 528, 540, 560, 576, 600, 624, 630, 648, 660, 704, 720, 726, 756, 768, 780, 792, 800, 810, 816, 832, 880, 912, 924, 936, 960, 990, 1008, 1014, 1020, 1040, 1050, 1092, 1104, 1134
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OFFSET

1,1


COMMENTS

Pseudoperfect numbers (A005835) that are exponentially odd (A268335) are also biunitary pseudoperfect numbers (A292985), since all of their divisors are biunitary.
First differs from A335216 at n = 28.


LINKS



EXAMPLE

48 is a term since it is not exponentially odd number (48 = 2^4 * 3 and 4 is even), so not all of its divisors are biunitary, and it is the sum of a subset of its biunitary divisors: 8 + 16 + 24 = 48.


MATHEMATICA

f[n_] := Select[Divisors[n], Function[d, CoprimeQ[d, n/d]]]; bdiv[m_] := Select[Divisors[m], Last@Intersection[f@#, f[m/#]] == 1 &]; bPspQ[n_] := Module[{d = Most @ bdiv[n], x}, SeriesCoefficient[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, n}], n] > 0]; expOddQ[n_] := AllTrue[Last /@ FactorInteger[n], OddQ]; Select[Range[1000], ! expOddQ[#] && bPspQ[#] &]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



