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A287681
Twin practical numbers: numbers k such that both k and k+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
OFFSET
1,1
COMMENTS
Melfi proved that this sequence is infinite.
LINKS
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 29 2017
STATUS
approved