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%I #12 Nov 11 2022 11:36:18
%S 2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,29,31,32,37,41,43,47,49,53,59,
%T 61,64,67,71,73,79,81,83,89,97,101,103,107,109,113,121,125,127,131,
%U 137,139,149,151,157,163,167,169,173,179,181,191,193,197,199,211,223,227,229
%N Numbers dividing p^6 for p a prime.
%C Numbers of form p^k for p a prime, 1 <= k <= 6.
%C The groups of these orders (up to a(54403784) = 1073741789 in version V2.13-4) form a class contained in the Small Groups Library of MAGMA; the number of groups of order a(n) is in A128604.
%H Klaus Brockhaus, <a href="/A128603/b128603.txt">Table of n, a(n) for n = 1..10000</a>
%H MAGMA Documentation, <a href="http://magma.maths.usyd.edu.au/magma/htmlhelp/text404.htm">Database of Small Groups</a>
%e 25 = 5^2 divides 5^6 = 15625, hence 25 is a term.
%t Take[Union[Flatten[Divisors/@(Prime[Range[50]]^6)]],70] (* _Harvey P. Dale_, Nov 11 2022 *)
%o (Magma) [ k: k in [1..233] | exists(t) {x: x in [t: t in [1..6] ] | IsPower(k, x) and IsPrime(Iroot(k, x)) } ];
%o (PARI) for(n=2, 233, if(isprime(n), print1(n, ","), k=ispower(n, &r); if(isprime(r)&&k<=6, print1(n, ","))))
%o (PARI) is(n)=my(t=isprimepower(n)); t && t<7 \\ _Charles R Greathouse IV_, Sep 18 2015
%Y Cf. A000001 (number of groups of order n), A000961 (prime powers), A128604.
%K nonn
%O 1,1
%A _Klaus Brockhaus_, Mar 13 2007
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