A322293 Integers k such that A322292(k) <= k.

6, 8, 12, 14, 18, 20, 24, 30, 32, 42, 44, 48, 60, 62, 72, 74, 84, 90, 102, 104, 108, 110, 114, 132, 140, 168, 182, 198, 200, 234, 240, 242, 270, 272, 282, 284, 312, 314, 318, 354, 360, 390, 420, 422, 434, 462, 464, 468, 510, 572, 648, 660, 662, 762, 840, 884, 888, 942, 1064

Offset

1,1

Comments

Erdos conjectures that this sequence is finite.

Links

Robert Israel, Table of n, a(n) for n = 1..100 (terms 1..98 from Michel Marcus)(all terms <= 10^8).

Paul Erdos, Some unconventional problems in number theory, Acta Mathematica Hungarica, 33(1):71-80, 1979. See p. 73.

Maple

N:= 10^6: # to get all terms <= N
Res:= 6: v:= 6:
for n from 7 to N do
  if not isprime(n-1) then v:= max(v, n-1 + min(numtheory:-factorset(n-1))) fi;
if v <= n then Res:= Res, n fi;
od:
Res; # Robert Israel, Dec 03 2018

Mathematica

f[n_] := Module[{smax = 0}, Do[If[CompositeQ[m],  smax = Max[smax, m + FactorInteger[m][[1, 1]]]], {m, 2, n-1}]; smax]; aQ[n_] := f[n]<=n; Select[Range[6, 1000], aQ] (* Amiram Eldar, Dec 02 2018 *)

Prog

(PARI) f(n) = {my(smax = 0); forcomposite(m=1, n-1, smax = max(smax, m + factor(m)[1, 1]); ); smax; } \\ A322292
isok(n) = f(n) <= n;

Crossrefs

Cf. A061228, A159475, A322292.

Sequence in context: A315857 A243937 A242058 * A366442 A109138 A315858

Adjacent sequences: A322290 A322291 A322292 * A322294 A322295 A322296

Keyword

nonn,more

Author

Michel Marcus, Dec 02 2018

Status

approved