A287683 5-tuples of practical numbers: numbers n such that n-6, n-2, n, n+2, n+6 are all practical numbers.

18, 30, 198, 306, 462, 1482, 2550, 4422, 17298, 23322, 23550, 40350, 52578, 67938, 88506, 92202, 96222, 123006, 131070, 219102, 226182, 237690, 277506, 312702, 359658, 432822, 526878, 533370, 584166, 659934, 1032858, 1051650, 1140414, 1142658, 1243170, 1255422

Offset: 1

Author

Amiram Eldar, May 29 2017

Keywords

• nonn

Comments

Melfi conjectured that this sequence is infinite.

Links

• Amiram Eldar and Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 100 terms from Amiram Eldar)
• Giuseppe Melfi, A survey on practical numbers, Rend. Sem. Mat. Univ. Pol. Torino, 53, (1995), 347-359.
• Giuseppe Melfi, On 5-tuples of twin practical numbers, Bollettino della Unione Matematica Italiana, Serie 8, Vol. 2-B, No. 3 (1999), pp. 723-734.
• Giuseppe Melfi, 5-uples of practical numbers

Crossrefs

Cf. A005153, A287681, A287682.

Programs

Mathematica

prQ[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]]];
quintupleQ[n_] := prQ[n-6]&&prQ[n-2]&&prQ[n]&&prQ[n+2]&&prQ[n+6];
a={}; k=8; While[Length[a]<100, If[quintupleQ[k], a=AppendTo[a,k]]; k+=2];a