A128301 Indices of squares (of primes) in the semiprimes.

1, 3, 9, 17, 40, 56, 90, 114, 164, 253, 289, 404, 484, 533, 634, 783, 973, 1031, 1233, 1373, 1452, 1683, 1842, 2112, 2483, 2676, 2779, 2995, 3108, 3320, 4124, 4384, 4775, 4926, 5593, 5741, 6172, 6644, 6962, 7448, 7955, 8108, 8978, 9147, 9512, 9697, 10842

Offset

1,2

Comments

A001358(a(n)) = A001248(n) = A000040(n)^2.

Numbers n with property that tau(semiprime(n)) is not semiprime. - Juri-Stepan Gerasimov, Oct 15 2010

Links

Zak Seidov, Table of n, a(n) for n = 1..10000

Example

a(4) = 17 as 49 = 7^2 = prime(4)^2, the fourth square in the semiprimes, is the seventeenth semiprime.

Mathematica

With[{sp=Select[Range[50000], PrimeOmega[#]==2&]}, Flatten[Table[ Position[ sp, Prime[ n]^2], {n, Floor[Sqrt[Length[sp]]]}]]] (* Harvey P. Dale, Nov 17 2014 *)

Prog

(Perl) -MMath::Pari=factorint, PARI -wle 'my $c = 0; my $s = PARI 1; while (1) { ++$s; my($sp, $si) = @{factorint($s)}; next if @$sp > 2; next if $si->[0] + (@$si > 1 ? $si->[1] : 0) != 2; ++$c; print "$s => $c" if @$sp == 1}' # Hugo van der Sanden, Sep 25 2007
(PARI) a(n)=my(s=0, i=0); n=prime(n)^2; forprime(p=2, sqrt(n), s+=primepi(n\p); i++); s - i * (i-1)/2
\\ Charles R Greathouse IV, Apr 21 2011

Crossrefs

Cf. A128302, A001358, A001248, A072000.

Sequence in context: A293423 A011755 A262466 * A348382 A176148 A206701

Adjacent sequences: A128298 A128299 A128300 * A128302 A128303 A128304

Keyword

nonn

Author

Rick L. Shepherd, Feb 25 2007

Status

approved