|
%I #13 Jun 20 2021 02:30:07
%S 4,8,9,25,27,32,49,64,121,125,169,243,256,289,343,361,512,529,729,841,
%T 961,1331,1369,1681,1849,2048,2197,2209,2809,3125,3481,3721,4489,4913,
%U 5041,5329,6241,6561,6859,6889,7921,9409,10201,10609,11449,11881,12167
%N Composite numbers whose square has a prime number of divisors.
%C Also prime powers p^e with 2e+1 prime. - _Charles R Greathouse IV_, Sep 18 2015
%H Charles R Greathouse IV, <a href="/A051676/b051676.txt">Table of n, a(n) for n = 1..10000</a>
%p 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
%t Select[Range[10^4], ! PrimeQ[ # ] && PrimeQ[DivisorSigma[0, #^2]] &]
%o (PARI) is(n)=my(e=isprimepower(n)); e>1 && isprime(2*e+1) \\ _Charles R Greathouse IV_, Sep 18 2015
%o (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
%Y Subsequence of A246547 and hence of A025475.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Nov 15 2001
|
