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A051676 Composite numbers n such that the number of divisors of n^2 is a prime. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A259183 A056166 A093771 * A114129 A053810 A076702

Adjacent sequences:  A051673 A051674 A051675 * A051677 A051678 A051679

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Nov 15 2001

STATUS

approved

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Last modified April 2 18:05 EDT 2020. Contains 333189 sequences. (Running on oeis4.)