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A061286
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Smallest integer for which the number of divisors is the n-th prime.
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33
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2, 4, 16, 64, 1024, 4096, 65536, 262144, 4194304, 268435456, 1073741824, 68719476736, 1099511627776, 4398046511104, 70368744177664, 4503599627370496, 288230376151711744, 1152921504606846976
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OFFSET
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1,1
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COMMENTS
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Seems to be the same as "Even numbers with prime number of divisors" - Jason Earls, Jul 04 2001
Except for the first term, smallest number == 1 (mod prime(n)) having n divisors (by Fermat's little theorem). - Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 20 2003
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LINKS
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FORMULA
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a(n) = 2^(prime(n)-1) = 2^A006093(n).
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MATHEMATICA
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Table[2^(p-1), {p, Table[Prime[n], {n, 1, 18}]}] (* Geoffrey Critzer, May 26 2013 *)
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PROG
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(PARI) forstep(n=2, 100000000, 2, x=numdiv(n); if(isprime(x), print(n)))
(Python)
from sympy import isprime, divisor_count as tau
[2] + [2**(2*n) for n in range(1, 33) if isprime(tau(2**(2*n)))] # Karl V. Keller, Jr., Jul 10 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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