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A283262
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Numbers n such that tau(n^2) is a prime.
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2
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2, 3, 4, 5, 7, 8, 9, 11, 13, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227
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OFFSET
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1,1
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COMMENTS
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tau(n) is the number of positive divisors of n (A000005).
Supersequence of A055638 (sigma(n^2) is prime).
Subsequence of A000961 (powers of primes).
Prime powers p^e with 2e+1 prime (e >= 1).
See A061285(n) = the smallest number k such that tau(k^2) = n-th prime.
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LINKS
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EXAMPLE
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tau(4^2) = tau(16) = 5 (prime).
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MAPLE
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N:= 1000: # to get all terms <= N
es:= select(t -> isprime(2*t+1), [$1..ilog2(N)]):
Ps:= select(isprime, [2, seq(i, i=3..N, 2)]):
sort(select(`<=`, [seq(seq(p^e, e=es), p=Ps)], N)): # Robert Israel, Mar 16 2017
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MATHEMATICA
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PROG
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(Magma) [n: n in [2..100000] | IsPrime(NumberOfDivisors(n^2))]
(PARI) for(n=1, 227, if(isprime(numdiv(n^2)), print1(n, ", "))) \\ Indranil Ghosh, Mar 09 2017
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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