

A322292


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


2



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
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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):7180, 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(n1) then V[n]:= V[n1]
else V[n]:= max(V[n1], n1+min(numtheory:factorset(n1)))
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, n1}]; smax]; Array[a, 100, 5] (* Amiram Eldar, Dec 02 2018 *)


PROG

(PARI) a(n) = {my(smax = 0); for(m=2, n1, 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



