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
Keywords
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
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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
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Mathematica
Select[Range[10^4], ! PrimeQ[ # ] && PrimeQ[DivisorSigma[0, #^2]] &]
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PARI
is(n)=my(e=isprimepower(n)); e>1 && isprime(2*e+1) \\ Charles R Greathouse IV, Sep 18 2015
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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
Comments