A341099 Numbers divisible by at least three terms of A008864.

12, 18, 24, 30, 32, 36, 40, 42, 48, 54, 56, 60, 64, 72, 80, 84, 88, 90, 96, 102, 104, 108, 112, 114, 120, 126, 128, 132, 136, 138, 140, 144, 150, 152, 156, 160, 162, 168, 174, 176, 180, 186, 192, 196, 198, 200, 204, 208, 210, 216, 220, 222, 224, 228, 234, 240, 248, 252, 256, 258, 264, 270, 272

Offset: 1

Author

J. M. Bergot and Robert Israel, Feb 04 2021

Keywords

• nonn

Comments

Numbers divisible by p+1 for at least three primes p.

Numbers k with A072627(k) >= 3.

Every positive multiple of a term is a term.

Examples

			a(4) = 30 is a term because it is divisible by 2+1=3, 5+1=6 and 29+1=30.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005101, A005835, A008864, A072627.

Programs

Maple

filter:= proc(n) local D;
  D:= convert(numtheory:-divisors(n),list);
  numboccur(true, map(t -> isprime(t-1),D))>= 3
end proc:
select(filter, [$1..1000]);

Mathematica

okQ[n_] := DivisorSum[n, Boole[PrimeQ[#-1]]&] >= 3;
Select[Range[1000], okQ] (* Jean-François Alcover, May 16 2023 *)

PARI

isok(m) = sumdiv(m, d, isprime(d-1)) >= 3; \\ Michel Marcus, Feb 05 2021