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A113877
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Semiprimes to semiprime powers.
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5
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256, 1296, 4096, 6561, 10000, 46656, 262144, 531441, 1048576, 10077696, 60466176, 268435456, 387420489, 1000000000, 1073741824, 3486784401, 78364164096
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| This is the semiprime analogue of A113854 (numbers of the form p^q where p and q are primes).
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FORMULA
| {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}.
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EXAMPLE
| 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.
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CROSSREFS
| Cf. A000040, A001358, A113854.
Sequence in context: A206111 A120054 A129539 * A205097 A205090 A206327
Adjacent sequences: A113874 A113875 A113876 * A113878 A113879 A113880
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Jan 27 2006
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