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A283262
Numbers m such that tau(m^2) is a prime.
2
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
OFFSET
1,1
COMMENTS
tau(m) is the number of positive divisors of m (A000005).
Numbers m such that A000005(A000290(m)) = A048691(m) is a prime.
Union of A000040 (primes) and A051676.
Supersequence of A055638 (sigma(m^2) is prime).
Subsequence of A000961 (powers of primes).
Prime powers p^e with 2e+1 prime (e >= 1).
See A061285(m) = the smallest number k such that tau(k^2) = m-th prime.
LINKS
EXAMPLE
tau(4^2) = tau(16) = 5 (prime).
MAPLE
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
MATHEMATICA
Select[Range@ 227, PrimeQ[DivisorSigma[0, #^2]] &] (* Michael De Vlieger, Mar 09 2017 *)
PROG
(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
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Mar 08 2017
STATUS
approved