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 A287679 Practical Pell numbers. 2
 1, 2, 12, 408, 13860, 470832, 15994428, 543339720, 18457556052, 627013566048, 21300003689580, 723573111879672, 24580185800219268, 835002744095575440, 963592443113182178088, 32733777552734744709300, 1111984844349868137938112, 1283229546787304717998403160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Melfi proved that this sequence is infinite. The indices of these Pell numbers are 1, 2, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 56, 60, 64, 72, 80, 84, 88, 96, 100, 104, 108, 112, 120, 128, 132, 136, 140, 144, 152, 156, 160, 168, 176, ... LINKS Amiram Eldar, Table of n, a(n) for n = 1..37 Giuseppe Melfi, A survey on practical numbers, Rend. Sem. Mat. Univ. Pol. Torino, 53, (1995), 347-359. EXAMPLE 12 is in this sequence since it is the 4th Pell number, A000129(4) and is also a practical number, A005153(6). MATHEMATICA PracticalQ[n_] := Module[{f, p, e, prod=1, ok=True}, If[n<1 || (n>1 && OddQ[n]), False, If[n==1, True, f=FactorInteger[n]; {p, e} = Transpose[f]; Do[If[p[[i]] > 1+DivisorSigma[1, prod], ok=False; Break[]]; prod=prod*p[[i]]^e[[i]], {i, Length[p]}]; ok]]]; Select[LinearRecurrence[{2, 1}, {1, 2}, 150], PracticalQ] CROSSREFS Cf. A000129, A005153, A124105, A287677. Sequence in context: A012551 A156509 A229919 * A051009 A324616 A060942 Adjacent sequences:  A287676 A287677 A287678 * A287680 A287681 A287682 KEYWORD nonn AUTHOR Amiram Eldar, May 29 2017 STATUS approved

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Last modified November 28 04:31 EST 2021. Contains 349400 sequences. (Running on oeis4.)