login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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