%I #29 Jul 23 2024 15:03:58
%S 1,3,9,17,40,56,90,114,164,253,289,404,484,533,634,783,973,1031,1233,
%T 1373,1452,1683,1842,2112,2483,2676,2779,2995,3108,3320,4124,4384,
%U 4775,4926,5593,5741,6172,6644,6962,7448,7955,8108,8978,9147,9512,9697,10842
%N Indices of squares (of primes) in the semiprimes.
%C A001358(a(n)) = A001248(n) = A000040(n)^2.
%C Numbers n with property that tau(semiprime(n)) is not semiprime. - _Juri-Stepan Gerasimov_, Oct 15 2010
%H Zak Seidov, <a href="/A128301/b128301.txt">Table of n, a(n) for n = 1..10000</a>
%e a(4) = 17 as 49 = 7^2 = prime(4)^2, the fourth square in the semiprimes, is the seventeenth semiprime.
%t 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 *)
%o (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
%o (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
%o \\ _Charles R Greathouse IV_, Apr 21 2011
%o (Python)
%o from math import isqrt
%o from sympy import prime, primepi
%o def A128301(n):
%o m = prime(n)**2
%o return int(sum(primepi(m//prime(k))-k+1 for k in range(1,n+1))) # _Chai Wah Wu_, Jul 23 2024
%Y Cf. A128302, A001358, A001248, A072000.
%K nonn
%O 1,2
%A _Rick L. Shepherd_, Feb 25 2007