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

5,1

Comments

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

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.

Example

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

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 *)

Prog

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

Crossrefs

Cf. A061228, A159475, A322293.

Sequence in context: A088684 A088683 A201578 * A195707 A175217 A000509

Adjacent sequences: A322289 A322290 A322291 * A322293 A322294 A322295

Keyword

nonn

Author

Michel Marcus, Dec 02 2018

Status

approved