A283262 Numbers m such that tau(m^2) is a prime.

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

Author

Jaroslav Krizek, Mar 08 2017

Keywords

• nonn

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.

Examples

			tau(4^2) = tau(16) = 5 (prime).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000290, A000961, A048691, A051676, A055638, A061285.

Programs

Magma

[n: n in [2..100000] | IsPrime(NumberOfDivisors(n^2))];

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 *)

PARI

isok(n)=isprime(numdiv(n^2)) \\ Indranil Ghosh, Mar 09 2017