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A341099 Numbers divisible by at least three terms of A008864.

%I A341099 #21 May 16 2023 10:39:42
%S A341099 12,18,24,30,32,36,40,42,48,54,56,60,64,72,80,84,88,90,96,102,104,108,
%T A341099 112,114,120,126,128,132,136,138,140,144,150,152,156,160,162,168,174,
%U A341099 176,180,186,192,196,198,200,204,208,210,216,220,222,224,228,234,240,248,252,256,258,264,270,272
%N A341099 Numbers divisible by at least three terms of A008864.
%C A341099 Numbers divisible by p+1 for at least three primes p.
%C A341099 Numbers k with A072627(k) >= 3.
%C A341099 Every positive multiple of a term is a term.
%H A341099 Robert Israel, <a href="/A341099/b341099.txt">Table of n, a(n) for n = 1..10000</a>
%e A341099 a(4) = 30 is a term because it is divisible by 2+1=3, 5+1=6 and 29+1=30.
%p A341099 filter:= proc(n) local D;
%p A341099   D:= convert(numtheory:-divisors(n),list);
%p A341099   numboccur(true, map(t -> isprime(t-1),D))>= 3
%p A341099 end proc:
%p A341099 select(filter, [$1..1000]);
%t A341099 okQ[n_] := DivisorSum[n, Boole[PrimeQ[#-1]]&] >= 3;
%t A341099 Select[Range[1000], okQ] (* _Jean-François Alcover_, May 16 2023 *)
%o A341099 (PARI) isok(m) = sumdiv(m, d, isprime(d-1)) >= 3; \\ _Michel Marcus_, Feb 05 2021
%Y A341099 Cf. A005101, A005835, A008864, A072627.
%K A341099 nonn
%O A341099 1,1
%A A341099 _J. M. Bergot_ and _Robert Israel_, Feb 04 2021