

A118672


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


1



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
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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: A182339 A110262 A176693 * A100417 A333337 A070089
Adjacent sequences: A118669 A118670 A118671 * A118673 A118674 A118675


KEYWORD

nonn


AUTHOR

Franklin T. AdamsWatters, May 19 2006


EXTENSIONS

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


STATUS

approved



