|
|
A118672
|
|
Numbers divisible by prime(i)^i for some i.
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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:
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|