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A100716
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Numbers k such that p^p divides k for some prime p.
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29
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4, 8, 12, 16, 20, 24, 27, 28, 32, 36, 40, 44, 48, 52, 54, 56, 60, 64, 68, 72, 76, 80, 81, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 135, 136, 140, 144, 148, 152, 156, 160, 162, 164, 168, 172, 176, 180, 184, 188, 189, 192, 196, 200, 204, 208, 212
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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a(n) ~ k*n with k = 1/(1 - Product(1 - p^-p)) = 3.5969959469... where the product is over all primes p. - Charles R Greathouse IV, Jan 24 2012
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EXAMPLE
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54 is included because 3^3 divides 54.
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MATHEMATICA
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fQ[n_] := Union[ Table[ #[[1]] <= #[[2]]] & /@ FactorInteger[n]][[ -1]] == True; Select[ Range[2, 215], fQ[ # ] &] (* Robert G. Wilson v, Dec 14 2004 *)
f[n_] := Module[{aux=FactorInteger[n]}, Last@Union@Table[aux[[i, 1]] <= aux[[i, 2]], {i, Length[aux]}] == True]; Select[Range[2, 215], f] (* José María Grau Ribas, Jan 25 2012 *)
Rest@ Select[Range@ 216, Times @@ Boole@ Map[First@ # > Last@ # &, FactorInteger@ #] == 0 &] (* Michael De Vlieger, Aug 19 2016 *)
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PROG
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(PARI) is(n)=forprime(p=2, default(primelimit), if(n%p^p==0, return(1)); if(p^p>n, return(0))) \\ Charles R Greathouse IV, Jan 24 2012
(Haskell)
a100716 n = a100716_list !! (n-1)
a100716_list = filter (\x -> or $
zipWith (<=) (a027748_row x) (map toInteger $ a124010_row x)) [1..]
(Scheme, with Antti Karttunen's IntSeq-library)
(Python)
from itertools import count, islice
from sympy import factorint
def A100716_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:any(map(lambda d:d[1]>=d[0], factorint(n).items())), count(max(startvalue, 1)))
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CROSSREFS
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Subsequence of A276079 from which it differs for the first time at n=175, where a(175) = 628, while A276079(175) = 625, a value missing from here.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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