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.
Giuseppe Melfi, 5-uples of practical numbers
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