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A287682 Triples of practical numbers: numbers n such that n-2, n, n+2 are all practical numbers. 3
4, 6, 18, 30, 198, 306, 462, 702, 1482, 2550, 3330, 4422, 5778, 6102, 6498, 9042, 11178, 11778, 14418, 15498, 17298, 17442, 19458, 20862, 21582, 22878, 23322, 23550, 25230, 26622, 26862, 26910, 27378, 30210, 34542, 36738, 38610, 39006, 39102, 40350, 40662 (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 survey on practical numbers, Rend. Sem. Mat. Univ. Pol. Torino, 53, (1995), 347-359.

Giuseppe Melfi, Triplets of 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; p2=False; k=2; While[Length[a]<100, p3=practicalQ[k]; If[p1 && p2 && p3, a=AppendTo[a, k-2]]; p1 = p2; p2 = p3; k+=2]; a

CROSSREFS

Cf. A005153, A209236, A287681, A287683.

Sequence in context: A026623 A026689 A138276 * A209236 A182643 A156096

Adjacent sequences:  A287679 A287680 A287681 * A287683 A287684 A287685

KEYWORD

nonn

AUTHOR

Amiram Eldar, May 29 2017

STATUS

approved

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Last modified February 23 12:38 EST 2020. Contains 332159 sequences. (Running on oeis4.)