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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:
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
Complement of A325128.
Sequence in context: A110262 A176693 A352872 * A100417 A333337 A070089
KEYWORD
nonn
AUTHOR
EXTENSIONS
An incorrect g.f. was deleted by N. J. A. Sloane, Sep 13 2009
STATUS
approved

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)