A334899 Bi-unitary practical numbers (A334898) that are not exponentially odd numbers (A268335).

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

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