A334899 - OEIS

%I #10 May 17 2020 02:15:45

%S 48,72,192,240,288,320,336,360,432,448,504,528,600,624,648,768,792,

%T 800,810,816,912,936,960,1050,1104,1134,1152,1176,1200,1224,1280,1296,

%U 1344,1350,1368,1392,1400,1440,1470,1488,1568,1650,1656,1680,1728,1776,1782,1792

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

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

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

%H Amiram Eldar, <a href="/A334899/b334899.txt">Table of n, a(n) for n = 1..850</a>

%t 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[#] &]

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

%K nonn

%O 1,1

%A _Amiram Eldar_, May 16 2020