A322292 a(n) = Max_{c composite, c < n} (c + least prime factor of c).

6, 6, 8, 8, 10, 12, 12, 12, 14, 14, 16, 18, 18, 18, 20, 20, 22, 24, 24, 24, 26, 30, 30, 30, 30, 30, 32, 32, 34, 36, 36, 40, 40, 40, 40, 42, 42, 42, 44, 44, 46, 48, 48, 48, 50, 56, 56, 56, 56, 56, 56, 60, 60, 60, 60, 60, 62, 62, 64, 66, 66, 70, 70, 70, 70, 72, 72, 72

Offset: 5

Author

Michel Marcus, Dec 02 2018

Keywords

• nonn

Comments

a(n) is only defined for n >= 5, because for n < 5, the condition {c composite, c < n} results in the empty set.

Examples

			a(5) = 6 because the largest composite c < n = 5 is 4, which has the largest prime factor 2. Hence a(5) = 4 + 2 = 6. - _David A. Corneth_, Dec 03 2018
		

Links

• Robert Israel, Table of n, a(n) for n = 5..10000
• Paul Erdos, Some unconventional problems in number theory, Acta Mathematica Hungarica, 33(1):71-80, 1979. See p. 73.

Crossrefs

Cf. A061228, A159475, A322293.

Programs

Maple

N:= 100: # to get a(5)..a(N)
V:= Vector(N):
V[5]:= 6;
for n from 6 to N do
  if isprime(n-1) then V[n]:= V[n-1]
  else V[n]:= max(V[n-1],n-1+min(numtheory:-factorset(n-1)))
  fi
od:
convert(V[5..N],list); # Robert Israel, Dec 03 2018

Mathematica

a[n_] := Module[{smax = 0}, Do[If[CompositeQ[m],  smax = Max[smax, m + FactorInteger[m][[1, 1]]]], {m, 2, n-1}]; smax]; Array[a, 100, 5] (* Amiram Eldar, Dec 02 2018 *)

PARI

a(n) = {my(smax = 0); for(m=2, n-1, if (!isprime(m), smax = max(smax, m + factor(m)[1, 1]); )); smax; }