OFFSET
1,1
COMMENTS
Numbers of form p^k for p a prime, 1 <= k <= 6.
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.
LINKS
Klaus Brockhaus, Table of n, a(n) for n = 1..10000
MAGMA Documentation, Database of Small Groups
EXAMPLE
25 = 5^2 divides 5^6 = 15625, hence 25 is a term.
MATHEMATICA
Take[Union[Flatten[Divisors/@(Prime[Range[50]]^6)]], 70] (* Harvey P. Dale, Nov 11 2022 *)
PROG
(Magma) [ k: k in [1..233] | exists(t) {x: x in [t: t in [1..6] ] | IsPower(k, x) and IsPrime(Iroot(k, x)) } ];
(PARI) for(n=2, 233, if(isprime(n), print1(n, ", "), k=ispower(n, &r); if(isprime(r)&&k<=6, print1(n, ", "))))
(PARI) is(n)=my(t=isprimepower(n)); t && t<7 \\ Charles R Greathouse IV, Sep 18 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Klaus Brockhaus, Mar 13 2007
STATUS
approved