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%I #8 Jul 02 2020 03:51:48
%S 48,60,72,80,90,150,162,192,240,288,294,320,336,360,420,432,448,504,
%T 528,540,560,576,600,624,630,648,660,704,720,726,756,768,780,792,800,
%U 810,816,832,880,912,924,936,960,990,1008,1014,1020,1040,1050,1092,1104,1134
%N Bi-unitary pseudoperfect numbers (A292985) that are not exponentially odd numbers (A268335).
%C Pseudoperfect numbers (A005835) that are exponentially odd (A268335) are also bi-unitary pseudoperfect numbers (A292985), since all of their divisors are bi-unitary.
%C First differs from A335216 at n = 28.
%H Amiram Eldar, <a href="/A335938/b335938.txt">Table of n, a(n) for n = 1..3000</a>
%e 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 bi-unitary, and it is the sum of a subset of its bi-unitary divisors: 8 + 16 + 24 = 48.
%t 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[#] &]
%Y Subsequence of A005835 and A292985.
%Y Cf. A222266, A268335, A295830, A335216.
%K nonn
%O 1,1
%A _Amiram Eldar_, Jun 30 2020
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