OFFSET
1,1
COMMENTS
The following is a quotation from Hage-Hassan in his paper (see Link below). "The (concept of) right and left symmetry is fundamental in physics. This incites us to ask whether this symmetry is in (the) primes. Find the numbers n with a + a' = n. a, a' are primes and {a} are all the primes with: n/2 <= a < n and n = 2,3, ..."
LINKS
Mehdi Hage-Hassan, An elementary introduction to Quantum mechanic, hal-00879586 2013 pp 58.
EXAMPLE
a(13)=24, because the practical numbers p in the range 12 <= p < 24 are {12, 16, 18, 20}. Also the complementary set {12, 8, 6, 4} has all its members practical numbers. This is the 13th occurrence of such a number.
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]]];
plst[n_] := Select[Range[Ceiling[n/2], n-1], PracticalQ]; lst={}; Do[If[plst[n]!={}&&AllTrue[n-plst[n], PracticalQ], AppendTo[lst, n]], {n, 1, 10000}]; lst
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Frank M Jackson, Dec 18 2018
STATUS
approved