A051676 Composite numbers whose square has a prime number of divisors.

4, 8, 9, 25, 27, 32, 49, 64, 121, 125, 169, 243, 256, 289, 343, 361, 512, 529, 729, 841, 961, 1331, 1369, 1681, 1849, 2048, 2197, 2209, 2809, 3125, 3481, 3721, 4489, 4913, 5041, 5329, 6241, 6561, 6859, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12167

Offset

1,1

Comments

Also prime powers p^e with 2e+1 prime. - Charles R Greathouse IV, Sep 18 2015

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Maple

with(numtheory): A051676 := proc(n) option remember: local k: if(n=1)then return 4: fi: for k from procname(n-1)+1 do if(not isprime(k) and isprime(tau(k^2)))then return k: fi: od: end: seq(A051676(n), n=1..47); # Nathaniel Johnston, May 26 2011

Mathematica

Select[Range[10^4], ! PrimeQ[ # ] && PrimeQ[DivisorSigma[0, #^2]] &]

Prog

(PARI) is(n)=my(e=isprimepower(n)); e>1 && isprime(2*e+1) \\ Charles R Greathouse IV, Sep 18 2015
(PARI) list(lim)=my(v=List(apply(p->p^2, primes(sqrtint(lim\=1)))), e); forprime(q=7, 2*logint(lim, 2)+1, e=q\2; forprime(p=2, sqrtnint(lim, e), listput(v, p^e))); Set(v) \\ Charles R Greathouse IV, Sep 18 2015

Crossrefs

Subsequence of A246547 and hence of A025475.

Sequence in context: A056166 A093771 A371223 * A114129 A053810 A076702

Adjacent sequences: A051673 A051674 A051675 * A051677 A051678 A051679

Keyword

nonn

Author

Robert G. Wilson v, Nov 15 2001

Status

approved