

A351166


a(1)=1; for n > 1, a(n) is the smallest number that has n divisors and is coprime to a(n1).


0



1, 2, 9, 8, 81, 20, 729, 40, 441, 80, 59049, 140, 531441, 320, 3969, 440, 43046721, 700, 387420489, 560, 88209, 5120, 31381059609, 1120, 1185921, 20480, 53361, 4160, 22876792454961, 2800, 205891132094649, 3080, 9979281, 327680, 1750329, 8800, 150094635296999121
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OFFSET

1,2


COMMENTS

For every odd prime p, a(p) = 3^(p1).
For n > 1, the smallest prime factor of a(n) is 2 + (n mod 2); see Examples.
For n > 4, a(n) is a multiple of 5 iff n is even.
Is 4 the largest composite m such that a(m) is a prime power?


LINKS



EXAMPLE

Given that a(27) = 53361 = 3^2 * 7^2 * 11^2, the prime factors of a(28) cannot include 3, 7, or 11, so the smallest primes available as prime factors of a(28) are 2, 5, and 13. The only prime signatures yielding 28 divisors are p^27, p^13 * q, p^6 * q^3, and p^6 * q * r, and the smallest candidate value with each of these signatures is 2^27 = 134217728, 2^13 * 5 = 40960, 2^6 * 5^3 = 8000, and 2^6 * 5 * 13 = 4160. The smallest of these is 4160, so a(28) = 4160. (This is the smallest term that is a multiple of 13.)
The table below lists the first several terms and their prime factorizations.
n a(n)
 
1 1 = 1
2 2 = 2^1
3 9 = 3^2
4 8 = 2^3
5 81 = 3^4
6 20 = 2^2 * 5^1
7 729 = 3^6
8 40 = 2^3 * 5^1
9 441 = 3^2 * 7^2
10 80 = 2^4 * 5^1


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



