A287682 Triples of practical numbers: numbers n such that n-2, n, n+2 are all practical numbers.

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

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