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A064182
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Sum_{k <= 10^n} number of distinct primes dividing k (A001221).
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1
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0, 11, 171, 2126, 24300, 266400, 2853708, 30130317, 315037281, 3271067968, 33787242719
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| This is just a subsequence of A013939. - N. J. A. Sloane, Jul 16 2011.
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FORMULA
| a(n) = Sum_{k, 1, limit}, PrimePi(10^n/k); which seems to be about 10^n/2.
On the contrary, I guess that a(n) ~ 10^n * log n. [Charles R Greathouse IV, Jul 13 2011]
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MATHEMATICA
| s = 0; k = 2; Do[ While[ k <= 10^n, s = s + PrimeNu@ k; k++ ]; Print[ s], {n, 8}]
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PROG
| (PARI) a(n)=sum(k=1, 10^n, omega(k)) \\ Charles R Greathouse IV, Jul 13 2011
(PARI) a(n)=sum(k=1, 10^n\2, primepi(10^n\k)) \\ Charles R Greathouse IV, Jul 13 2011
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CROSSREFS
| Cf. A001221.
Sequence in context: A157944 A167245 A205087 * A139792 A025758 A141955
Adjacent sequences: A064179 A064180 A064181 * A064183 A064184 A064185
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 20 2001
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