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

1,1

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

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 *)

Crossrefs

Cf. A067808.

Sequence in context: A137493 A179669 A067808 * A291804 A131663 A090392

Adjacent sequences: A302124 A302125 A302126 * A302128 A302129 A302130

Keyword

nonn

Author

Robert Israel, Jun 20 2018

Status

approved