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A120632
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Number of numbers >1 up to 2*prime(n) which are divisible by primes up to prime(n).
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4
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2, 4, 8, 11, 18, 22, 29, 33, 40, 51, 54, 64, 72, 76, 84, 94, 104, 109, 120, 127, 132, 142, 150, 161, 174, 181, 186, 194, 199, 207, 230, 238, 248, 252, 270, 275, 285, 297, 305, 317, 327, 331, 349, 353, 361, 365, 386, 407, 415, 419, 426, 438, 442, 460, 471, 482
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OFFSET
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1,1
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COMMENTS
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The first prime(n+1)-2 numbers >1 are divisible by primes up to prime(n).
Complement of A137624; A137621(a(n))=A000040(n); A137621(a(n)+1)=A100484(n). - Reinhard Zumkeller, Jan 30 2008
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LINKS
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Robert Israel, Table of n, a(n) for n = 1..10000
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FORMULA
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a(n) = A120633(n) + A040976(n+1) = A076274(n) - A070046(n).
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EXAMPLE
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a(4)=11 because exactly 11 numbers between 2 and 2*prime(4)=2*7=14, namely: 2,3,4,5,6,7,8,9,10,12,14 are divisible by the first four primes 2,3,5,7.
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MAPLE
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f:= proc(n) local p;
p:= ithprime(n); 2*p - numtheory:-pi(2*p)+n-1
end proc:
map(f, [$1..100]); # Robert Israel, Mar 02 2022
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PROG
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(PARI) a(n) = {nb = 0; for (i = 2, 2*prime(n), for (ip = 1, n, if ( !(i % prime(ip)), nb++; break; ); ); ); nb; } \\ Michel Marcus, Oct 26 2013
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CROSSREFS
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Cf. A000040, A100484, A137621, A137624.
Cf. A120633, A040976, A076274, A070046.
Sequence in context: A279098 A010068 A295674 * A007295 A053439 A337501
Adjacent sequences: A120629 A120630 A120631 * A120633 A120634 A120635
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy, Jun 21 2006
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STATUS
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approved
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