A128603 Numbers dividing p^6 for p a prime.

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, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 101, 103, 107, 109, 113, 121, 125, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229

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

Cf. A000001 (number of groups of order n), A000961 (prime powers), A128604.

Sequence in context: A036116 A246655 A000961 * A195943 A096165 A164336

Adjacent sequences: A128600 A128601 A128602 * A128604 A128605 A128606

Keyword

nonn

Author

Klaus Brockhaus, Mar 13 2007

Status

approved