A287681 Twin practical numbers: numbers k such that both k and k+2 are practical numbers.

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

Offset

1,1

Comments

Melfi proved that this sequence is infinite.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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: A358126 A096174 A096173 * A333021 A114874 A100361

Adjacent sequences: A287678 A287679 A287680 * A287682 A287683 A287684

Keyword

nonn

Author

Amiram Eldar, May 29 2017

Status

approved