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A334900
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Numbers k such that k and k+2 are both bi-unitary practical numbers (A334898).
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2
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6, 30, 40, 54, 510, 544, 798, 918, 928, 1120, 1240, 1288, 1408, 1480, 1566, 1672, 1720, 1768, 1792, 1888, 1950, 1974, 2046, 2430, 2440, 2560, 2728, 2814, 2838, 2968, 3198, 3318, 4134, 4158, 4264, 4422, 4480, 4758, 5248, 6102, 6270, 6424, 6942, 7590, 7830, 9280
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OFFSET
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1,1
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LINKS
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EXAMPLE
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6 is a term since 6 and 6 + 2 = 8 are both bi-unitary practical numbers.
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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