OFFSET
1,1
COMMENTS
Melfi proved that this sequence is infinite.
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.
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, May 29 2017
STATUS
approved