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A246547 Prime powers p^e where p is a prime and e >= 2 (prime powers without the primes or 1). 26
4, 8, 9, 16, 25, 27, 32, 49, 64, 81, 121, 125, 128, 169, 243, 256, 289, 343, 361, 512, 529, 625, 729, 841, 961, 1024, 1331, 1369, 1681, 1849, 2048, 2187, 2197, 2209, 2401, 2809, 3125, 3481, 3721, 4096, 4489, 4913, 5041, 5329, 6241, 6561, 6859, 6889, 7921, 8192, 9409, 10201, 10609, 11449, 11881, 12167, 12769, 14641 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

These are sometimes called the proper prime powers.

A proper subset of A001597.

LINKS

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

FORMULA

a(n)=A025475(n+1). A246547 = A000961 \ A008578 = { x in A001597 | A001221(x)=1 }. - M. F. Hasler, Aug 29 2014

MAPLE

isA246547 := proc(n)

    local ifs;

    ifs := ifactors(n)[2] ;

    if nops(ifs) <> 1 then

        false;

    else

        if op(2, op(1, ifs)) > 1 then

            true;

        else

            false;

        end if;

    end if;

end proc:

for n from 2 do

    if isA246547(n) then

        print(n) ;

    end if;

end do: # R. J. Mathar, Feb 01 2016

MATHEMATICA

With[{upto=15000}, Complement[Select[Range[upto], PrimePowerQ], Prime[ Range[ PrimePi[ upto]]]]] (* Harvey P. Dale, Nov 28 2014 *)

Select[ Range@ 15000, PrimePowerQ@# && !SquareFreeQ@# &] (* Robert G. Wilson v, Dec 01 2014 *)

PROG

(PARI) for(n=1, 10^5, if(isprimepower(n)>=2, print1(n, ", ")));

(PARI) m=10^5; v=[]; forprime(p=2, sqrtint(m), e=2; while(p^e<=m, v=concat(v, p^e); e++)); v=vecsort(v) \\ Faster program. Jens Kruse Andersen, Aug 29 2014

CROSSREFS

Essentially the same as A025475.

Cf. A000961, A001597, A025528, A246655.

Sequence in context: A134611 A134612 A025475 * A195942 A125643 A002760

Adjacent sequences:  A246544 A246545 A246546 * A246548 A246549 A246550

KEYWORD

nonn

AUTHOR

Joerg Arndt, Aug 29 2014

STATUS

approved

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Last modified May 29 21:28 EDT 2017. Contains 287257 sequences.