prog.sf

#!/usr/bin/ruby

# Where 11^n occurs in n-almost-primes, starting at a(0)=1.
# https://oeis.org/A078846

# New terms:
#   a(16) = 8683388113017
#   a(17) = 50433408838966

# Known terms:
#   1, 5, 40, 328, 2556, 18452, 126096, 827901, 5276913, 32887213, 201443165, 1217389949, 7279826998, 43168558912, 254258462459, 1489291941733

#`(
# PARI/GP program:

almost_prime_count(N, k) = if(k==1, return(primepi(N))); (f(m, p, k, j=0) = my(c=0, s=sqrtnint(N\m, k)); if(k==2, forprime(q=p, s, c += primepi(N\(m*q))-j; j += 1), forprime(q=p, s, c += f(m*q, q, k-1, j); j += 1)); c); f(1, 2, k);
a(n) = if(n == 0, 1, almost_prime_count(11^n, n)); \\ ~~~~

)

#   a(n) = my(x=2^n, y=2*x); while(1, my(v=count(x, y, n, n)); if(#v >= 1, return(v[1])); x=y+1; y=2*x); \\ ~~~~


for n in (0..100) {
    say [n, n.almost_prime_count(11**n)]
}

__END__
[0, 1]
[1, 5]
[2, 40]
[3, 328]
[4, 2556]
[5, 18452]
[6, 126096]
[7, 827901]
[8, 5276913]
[9, 32887213]
[10, 201443165]
[11, 1217389949]
[12, 7279826998]
[13, 43168558912]