cp's OEIS Frontend

A302127 Primitive terms of A067808.

%I A302127 #20 May 08 2021 08:28:06
%S A302127 720,1080,1680,1800,2016,2520,3024,3780,3960,4200,4680,5280,5544,6120,
%T A302127 6300,6840,7056,9240,9504,9600,10584,10920,11232,12480,12672,13104,
%U A302127 13200,13860,14256,14280,15600,16380,17136,19152,19656,20400,20592,21420,23184,23940,24000,25704,26928,28728,29232
%N A302127 Primitive terms of A067808.
%C A302127 Terms of A067808 that are not divisible by any smaller term of A067808.
%C A302127 For any set S of primes whose sum of reciprocals is infinite, there are members whose prime factors are all in S.  For example, by the strong form of Dirichlet's theorem this is the case for an arithmetic progression {x: x == c (mod d)} if c and d are coprime.
%H A302127 Robert Israel, <a href="/A302127/b302127.txt">Table of n, a(n) for n = 1..10000</a>
%p A302127 count:= 0: Res:= NULL:
%p A302127 for n from 1 while count < 100 do
%p A302127   F:= ifactors(n)[2];
%p A302127   if mul((t[1]^(t[2]+1)-1)^2/(t[1]^(2*t[2]+1)-1)/(t[1]-1), t = F) > 3 and andmap(s -> not(type(n/s,integer)), [Res]) then
%p A302127     count:= count+1; Res:= Res, n;
%p A302127   fi
%p A302127 od:
%p A302127 Res;
%t A302127 count = 0; Res = {};
%t A302127 For[n = 2, count < 100, n++, F = FactorInteger[n]; If[Product[{p, e} = pe; (p^(e+1)-1)^2/((p^(2e+1)-1)(p-1)), {pe, F}] > 3 && AllTrue[Res, !IntegerQ[n/#]&], count++; AppendTo[Res, n]]
%t A302127 ];
%t A302127 Res (* _Jean-François Alcover_, Apr 29 2019, after _Robert Israel_ *)
%Y A302127 Cf. A067808.
%K A302127 nonn
%O A302127 1,1
%A A302127 _Robert Israel_, Jun 20 2018