A287679 Practical Pell numbers.

1, 2, 12, 408, 13860, 470832, 15994428, 543339720, 18457556052, 627013566048, 21300003689580, 723573111879672, 24580185800219268, 835002744095575440, 963592443113182178088, 32733777552734744709300, 1111984844349868137938112, 1283229546787304717998403160

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