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
Keywords
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.
Programs
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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
Comments