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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.
3
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
1,1
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.
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 29 2017
STATUS
approved