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A048103
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Numbers not divisible by p^p for any prime p.
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8
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1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19, 21, 22, 23, 25, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 46, 47, 49, 50, 51, 53, 55, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 82, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 98
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OFFSET
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1,2
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COMMENTS
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If n = Product p_i^e_i then p_i>e_i for all i.
Complement of A100716; A129251(a(n)) = 0. - Reinhard Zumkeller, Apr 07 2007
Density is 0.72199023441955... = prod(1 - p^-p) where p runs over the primes. [Charles R Greathouse IV, Jan 25 2012]
A027748(a(n),k) <= A124010(a(n),k), 1<=k<=A001221(a(n)). [_Reinhard Zumkeller, Apr 28 2012_]
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) ~ kn with k = 1/prod(1 - p^-p) = prod 1 + 1/(p^p - 1) = 1.3850602852..., where the product is over all primes p. [Charles R Greathouse IV, Jan 25 2012]
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EXAMPLE
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6=2^1*3^1 is OK but 12=2^2*3^1 is not.
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PROG
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(Haskell)
a048103 n = a048103_list !! (n-1)
a048103_list = filter (\x -> and $
zipWith (>) (a027748_row x) (map toInteger $ a124010_row x)) [1..]
-- Reinhard Zumkeller, Apr 28 2012
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CROSSREFS
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Cf. A048102, A048104, A054743, A054744.
Sequence in context: A059557 A195291 A042968 * A193303 A092418 A004195
Adjacent sequences: A048100 A048101 A048102 * A048104 A048105 A048106
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KEYWORD
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nonn,easy,changed
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from James A. Sellers, Apr 22 2000
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STATUS
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approved
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