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A287681 Twin practical numbers: numbers n such that both n and n+2 are practical numbers. 8
2, 4, 6, 16, 18, 28, 30, 40, 54, 64, 78, 88, 126, 160, 196, 198, 208, 270, 304, 306, 340, 378, 390, 414, 448, 460, 462, 510, 520, 544, 558, 700, 702, 726, 798, 810, 858, 868, 880, 918, 928, 966, 990, 1024, 1120, 1216, 1230, 1240, 1288, 1300, 1350, 1408, 1456 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Melfi proved that this sequence is infinite.

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..1000

Giuseppe Melfi, A note on twin practical numbers, Le Matematiche, Vol. 57 No. 1 (2004), pp. 111-117.

Giuseppe Melfi, A survey on practical numbers, Rend. Sem. Mat. Univ. Pol. Torino, 53, (1995), 347-359.

Giuseppe Melfi, Twin practical numbers

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]]];

a={}; p1=False; k=2; While[Length[a]<100, p2=practicalQ[k]; If[p1 && p2, a=AppendTo[a, k-2]]; p1 = p2; k+=2]; a

CROSSREFS

Cf. A005153, A210479, A208249, A209236, A210480, A209236, A287682, A287683.

Sequence in context: A326782 A096174 A096173 * A333021 A114874 A100361

Adjacent sequences:  A287678 A287679 A287680 * A287682 A287683 A287684

KEYWORD

nonn

AUTHOR

Amiram Eldar, May 29 2017

STATUS

approved

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Last modified April 13 02:22 EDT 2021. Contains 342934 sequences. (Running on oeis4.)