1,1

This is the semiprime analogue of A113854 (numbers of the form p^q where p and q are primes).

{a(n)} = {a^b where a and b are elements of A001358}. {a(n)} = {(p*q)^(r*s) = (p^(r*s))*(q^r*s) for distinct primes p, q, r, s} UNION {(p*q)^(p*r) = (p^(p*r))*(q^(p*r)) for distinct primes p, q, r} UNION {(p*q)^(r*r) = (p^(r^2))*(q^(r^2)) for distinct primes p, q, r} UNION {(p*q)^(p*q)= (p^(p*q))*(q^(p*q)) for distinct primes p, q} UNION {(p^2)^(p^2) = p^(2*(p^2)) for prime p}.

a(1) = 256 = 4^4 = semiprime(1)^semiprime(1).

a(2) = 1296 = 6^4 = semiprime(2)^semiprime(1).

a(3) = 4096 = 4^6 = semiprime(1)^semiprime(2).

a(4) = 6561 = 9^4 = semiprime(3)^semiprime(1).

a(5) = 10000 = 10^4.

a(6) = 46656 = 6^6.

262144 = 4^9. 531441 = 9^6. 1048576 = 4^10. 10077696 = 6^9. 60466176 = 6^10. 268435456 = 4^14. 387420489 = 9^9. 1000000000 = 10^9. 1073741824 = 4^15. 3486784401 = 9^10. 78364164096 = 6^14.

Cf. A000040, A001358, A113854.

Sequence in context: A045034 A120054 A129539 this_sequence A014711 A014713 A016780

Adjacent sequences: A113874 A113875 A113876 this_sequence A113878 A113879 A113880

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 27 2006