A335938 Bi-unitary pseudoperfect numbers (A292985) that are not exponentially odd numbers (A268335).

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

Offset

1,1

Comments

Pseudoperfect numbers (A005835) that are exponentially odd (A268335) are also bi-unitary pseudoperfect numbers (A292985), since all of their divisors are bi-unitary.

First differs from A335216 at n = 28.

Links

Amiram Eldar, Table of n, a(n) for n = 1..3000

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 bi-unitary, and it is the sum of a subset of its bi-unitary 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

Subsequence of A005835 and A292985.

Cf. A222266, A268335, A295830, A335216.

Sequence in context: A259037 A231469 A261546 * A335216 A114821 A108098

Adjacent sequences: A335935 A335936 A335937 * A335939 A335940 A335941

Keyword

nonn

Author

Amiram Eldar, Jun 30 2020

Status

approved