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

Author

Amiram Eldar, May 29 2017

Keywords

• nonn

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

Crossrefs

Cf. A005153, A209236, A287681, A287683.

Programs

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