A334902 -id:A334902 - cp's OEIS frontend

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

Amiram Eldar, May 16 2020

nonn

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.

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

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

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[#] &]

cp's OEIS Frontend

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

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