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

1,1

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

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 *)

Crossrefs

Cf. A062457, A000040.

Complement of A325128.

Sequence in context: A110262 A176693 A352872 * A100417 A333337 A070089

Adjacent sequences: A118669 A118670 A118671 * A118673 A118674 A118675

Keyword

nonn

Author

Franklin T. Adams-Watters, May 19 2006

Extensions

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

Status

approved