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%I #9 May 17 2020 02:15:50
%S 6,30,40,54,510,544,798,918,928,1120,1240,1288,1408,1480,1566,1672,
%T 1720,1768,1792,1888,1950,1974,2046,2430,2440,2560,2728,2814,2838,
%U 2968,3198,3318,4134,4158,4264,4422,4480,4758,5248,6102,6270,6424,6942,7590,7830,9280
%N Numbers k such that k and k+2 are both bi-unitary practical numbers (A334898).
%H Amiram Eldar, <a href="/A334900/b334900.txt">Table of n, a(n) for n = 1..112</a>
%e 6 is a term since 6 and 6 + 2 = 8 are both bi-unitary practical numbers.
%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]; seq = {}; q1 = bPracQ[2]; Do[q2 = bPracQ[n]; If[q1 && q2, AppendTo[seq, n - 2]]; q1 = q2, {n, 4, 1000, 2}]; seq
%Y Cf. A287681, A330871, A334882, A334898, A334903.
%K nonn
%O 1,1
%A _Amiram Eldar_, May 16 2020
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