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

%I A287683 #10 May 30 2017 05:34:58
%S A287683 18,30,198,306,462,1482,2550,4422,17298,23322,23550,40350,52578,67938,
%T A287683 88506,92202,96222,123006,131070,219102,226182,237690,277506,312702,
%U A287683 359658,432822,526878,533370,584166,659934,1032858,1051650,1140414,1142658,1243170,1255422
%N A287683 5-tuples of practical numbers: numbers n such that n-6, n-2, n, n+2, n+6 are all practical numbers.
%C A287683 Melfi conjectured that this sequence is infinite.
%H A287683 Amiram Eldar and Giovanni Resta, <a href="/A287683/b287683.txt">Table of n, a(n) for n = 1..10000</a> (first 100 terms from Amiram Eldar)
%H A287683 Giuseppe Melfi, <a href="http://members.unine.ch/giuseppe.melfi/articoli/smapoto.pdf">A survey on practical numbers</a>, Rend. Sem. Mat. Univ. Pol. Torino, 53, (1995), 347-359.
%H A287683 Giuseppe Melfi, <a href="http://www.bdim.eu/item?id=BUMI_1999_8_2B_3_723_0">On 5-tuples of twin practical numbers</a>, Bollettino della Unione Matematica Italiana, Serie 8, Vol. 2-B, No. 3 (1999), pp. 723-734.
%H A287683 Giuseppe Melfi, <a href="http://www.dm.unipi.it/gauss-pages/melfi/public_html/quin.html">5-uples of practical numbers</a>
%t A287683 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]]];
%t A287683 quintupleQ[n_] := prQ[n-6]&&prQ[n-2]&&prQ[n]&&prQ[n+2]&&prQ[n+6];
%t A287683 a={}; k=8; While[Length[a]<100, If[quintupleQ[k], a=AppendTo[a,k]]; k+=2];a
%Y A287683 Cf. A005153, A287681, A287682.
%K A287683 nonn
%O A287683 1,1
%A A287683 _Amiram Eldar_, May 29 2017