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A246547 Prime powers p^e where p is a prime and e >= 2 (prime powers without the primes or 1). 47
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.

Equals A000961 \ A008578 = { x in A001597 | A001221(x)=1 }. - M. F. Hasler, Aug 29 2014

Composite numbers that are a multiple of their cototient. - Paolo P. Lava, Apr 18 2018

LINKS

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

FORMULA

a(n) = A025475(n+1). - M. F. Hasler, Aug 29 2014

MAPLE

isA246547 := proc(n)

    local ifs;

    ifs := ifactors(n)[2] ;

    if nops(ifs) <> 1 then

        false;

    else

        is(op(2, op(1, ifs)) > 1);

    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

# Alternative

with(numtheory): P:=proc(n) if not isprime(n) and frac(n/(n-phi(n)))=0

then n; fi; end: seq(P(i), i=4..10^4); # Paolo P. Lava, Apr 18 2018

# Or:

isA246547 := n -> not isprime(n) and nops(numtheory:-factorset(n)) = 1:

select(isA246547, [$1..10000]); # Peter Luschny, May 01 2018

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, A051953, A246655.

There are four different sequences which may legitimately be called "prime powers": A000961 (p^k, k >= 0), A246655 (p^k, k >= 1), A246547 (p^k, k >= 2), A025475 (p^k, k=0 and k >= 2). When you refer to "prime powers", be sure to specify which of these you mean. Also A001597 is the sequence of nontrivial powers n^k, n >= 1, k >= 2. - N. J. A. Sloane, Mar 24 2018

Sequence in context: A134611 A134612 A025475 * A195942 A125643 A002760

Adjacent sequences:  A246544 A246545 A246546 * A246548 A246549 A246550

KEYWORD

nonn,easy

AUTHOR

Joerg Arndt, Aug 29 2014

STATUS

approved

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Last modified May 24 13:22 EDT 2018. Contains 304524 sequences. (Running on oeis4.)