|
%I #13 Apr 06 2021 02:57:55
%S 2,4,6,8,9,10,12,14,16,18,20,22,24,26,27,28,30,32,34,36,38,40,42,44,
%T 45,46,48,50,52,54,56,58,60,62,63,64,66,68,70,72,74,76,78,80,81,82,84,
%U 86,88,90,92,94,96,98,99,100,102,104,106,108,110,112,114,116,117,118,120
%N Numbers divisible by prime(i)^i for some i.
%C Any multiple of an element of this sequence is in the sequence. The primitive elements of this sequence are A062457.
%C The asymptotic density of this sequence is 1 - Product_{k>=1} (1 - 1/prime(k)^k) = 0.55929756713969708790... - _Amiram Eldar_, Apr 06 2021
%H Robert Israel, <a href="/A118672/b118672.txt">Table of n, a(n) for n = 1..10000</a>
%p N:= 1000: # to get all terms <= N
%p S:= {}:
%p for i from 1 do
%p v:= ithprime(i)^i;
%p if v > N then break fi;
%p S:= S union {seq(j,j=v..N,v)};
%p od:
%p sort(convert(S,list)); # _Robert Israel_, Mar 27 2018
%t 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 *)
%Y Cf. A062457, A000040.
%Y Complement of A325128.
%K nonn
%O 1,1
%A _Franklin T. Adams-Watters_, May 19 2006
%E An incorrect g.f. was deleted by _N. J. A. Sloane_, Sep 13 2009
|
