A120033 Number of semiprimes s such that 2^n < s <= 2^(n+1).

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

Offset

0,4

Comments

The partial sum equals the number of Pi_2(2^n) = A125527(n).

Links

Dana Jacobsen, Table of n, a(n) for n = 0..62 (first 48 terms from Charles R Greathouse IV, corrected a(47)-a(48))

Example

(2^2, 2^3] there is one semiprime, namely 6. 4 was counted in the previous entry.

Mathematica

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

Prog

(PARI) pi2(n)=my(s, i); forprime(p=2, sqrt(n), s+=primepi(n\p); i++); s - i * (i-1)/2
a(n)=pi2(2^(n+1))-pi2(2^n) \\ Charles R Greathouse IV, May 15 2012
(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

Crossrefs

Cf. A001358, A072000, A066265, A036378, A120033-A120043.

Sequence in context: A331606 A079902 A309128 * A097073 A019085 A303644

Adjacent sequences: A120030 A120031 A120032 * A120034 A120035 A120036

Keyword

nonn

Author

Jonathan Vos Post and Robert G. Wilson v, Mar 20 2006

Status

approved