A118672 Numbers divisible by prime(i)^i for some i.

2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 27, 28, 30, 32, 34, 36, 38, 40, 42, 44, 45, 46, 48, 50, 52, 54, 56, 58, 60, 62, 63, 64, 66, 68, 70, 72, 74, 76, 78, 80, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 99, 100, 102, 104, 106, 108, 110, 112, 114, 116, 117, 118, 120

Offset: 1

Author

Franklin T. Adams-Watters, May 19 2006

Keywords

• nonn

Comments

Any multiple of an element of this sequence is in the sequence. The primitive elements of this sequence are A062457.

The asymptotic density of this sequence is 1 - Product_{k>=1} (1 - 1/prime(k)^k) = 0.55929756713969708790... - Amiram Eldar, Apr 06 2021

Links

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

Crossrefs

Cf. A062457, A000040.

Complement of A325128.

Programs

Maple

N:= 1000: # to get all terms <= N
S:= {}:
for i from 1 do
  v:= ithprime(i)^i;
  if v > N then break fi;
  S:= S union {seq(j,j=v..N,v)};
od:
sort(convert(S,list)); # Robert Israel, Mar 27 2018

Mathematica

seq[max_] := Module[{s = {}, p = 2, i = 1, q = 2}, While[q < max, s = Join[s, Range[q, max, q]]; p = NextPrime[p]; i++; q = p^i]; Union[s]]; seq[120] (* Amiram Eldar, Apr 06 2021 *)

Extensions

An incorrect g.f. was deleted by N. J. A. Sloane, Sep 13 2009