A302127 Primitive terms of A067808.

720, 1080, 1680, 1800, 2016, 2520, 3024, 3780, 3960, 4200, 4680, 5280, 5544, 6120, 6300, 6840, 7056, 9240, 9504, 9600, 10584, 10920, 11232, 12480, 12672, 13104, 13200, 13860, 14256, 14280, 15600, 16380, 17136, 19152, 19656, 20400, 20592, 21420, 23184, 23940, 24000, 25704, 26928, 28728, 29232

Offset: 1

Author

Robert Israel, Jun 20 2018

Keywords

• nonn

Comments

Terms of A067808 that are not divisible by any smaller term of A067808.

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.

Links

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

Crossrefs

Cf. A067808.

Programs

Maple

count:= 0: Res:= NULL:
for n from 1 while count < 100 do
  F:= ifactors(n)[2];
  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
    count:= count+1; Res:= Res, n;
  fi
od:
Res;

Mathematica

count = 0; Res = {};
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]]
];
Res (* Jean-François Alcover, Apr 29 2019, after Robert Israel *)