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A120033
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Number of semiprimes s such that 2^n < s <= 2^(n+1).
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15
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0, 1, 1, 4, 4, 12, 20, 40, 75, 147, 285, 535, 1062, 2006, 3918, 7548, 14595, 28293, 54761, 106452, 206421, 401522, 780966, 1520543, 2962226, 5777162, 11272279, 22009839, 43006972, 84077384, 164482781, 321944211, 630487562, 1235382703
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OFFSET
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0,4
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COMMENTS
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The partial sum equals the number of Pi_2(2^n) = A125527(n).
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LINKS
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EXAMPLE
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(2^2, 2^3] there is one semiprime, namely 6. 4 was counted in the previous entry.
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MATHEMATICA
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SemiPrimePi[n_] := Sum[PrimePi[n/Prime[i]] - i + 1, {i, PrimePi[Sqrt[n]]}]; t = Table[SemiPrimePi[2^n], {n, 0, 35}]; Rest@t - Most@t
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PROG
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(PARI) pi2(n)=my(s, i); forprime(p=2, sqrt(n), s+=primepi(n\p); i++); s - i * (i-1)/2
(Perl) use ntheory ":all"; print "$_ ", semiprime_count(1+(1<<$_), 1<<($_+1)), "\n" for 0..48; # Dana Jacobsen, Mar 04 2019
(Perl) use ntheory ":all"; my $l=0; for (0..48) { my $c=semiprime_count(1<<($_+1)); print "$_ ", $c-$l, "\n"; $l=$c; } # Dana Jacobsen, Mar 04 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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