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A334899 Bi-unitary practical numbers (A334898) that are not exponentially odd numbers (A268335). 2
48, 72, 192, 240, 288, 320, 336, 360, 432, 448, 504, 528, 600, 624, 648, 768, 792, 800, 810, 816, 912, 936, 960, 1050, 1104, 1134, 1152, 1176, 1200, 1224, 1280, 1296, 1344, 1350, 1368, 1392, 1400, 1440, 1470, 1488, 1568, 1650, 1656, 1680, 1728, 1776, 1782, 1792 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Practical numbers (A005153) that are exponentially odd (A268335) are also bi-unitary practical numbers (A334898), since all of their divisors are bi-unitary.

Of the first 2500 bi-unitary practical numbers, only 847 are in this sequence.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..850

MATHEMATICA

biunitaryDivisorQ[div_, n_] := If[Mod[#2, #1] == 0, Last @ Apply[Intersection, Map[Select[Divisors[#], Function[d, CoprimeQ[d, #/d]]] &, {#1, #2/#1}]] == 1, False] & @@ {div, n}; bdivs[n_] := Module[{d = Divisors[n]}, Select[d, biunitaryDivisorQ[#, n] &]]; bPracQ[n_] := Module[{d = bdivs[n], sd, x}, sd = Plus @@ d; Min @ CoefficientList[Series[Product[1 + x^d[[i]], {i, Length[d]}], {x, 0, sd}], x] >  0]; expOddQ[n_] := AllTrue[Last /@ FactorInteger[n], OddQ]; Select[Range[1000], !expOddQ[#] && bPracQ[#] &]

CROSSREFS

Cf. A005153, A268335, A287173, A334898, A334902.

Sequence in context: A124309 A112058 A033821 * A165039 A211721 A057533

Adjacent sequences:  A334896 A334897 A334898 * A334900 A334901 A334902

KEYWORD

nonn

AUTHOR

Amiram Eldar, May 16 2020

STATUS

approved

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Last modified September 27 11:57 EDT 2021. Contains 347689 sequences. (Running on oeis4.)