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A056652 Integers > 1 whose prime divisors are all Mersenne primes (i.e. of the form (2^p -1)). 4
3, 7, 9, 21, 27, 31, 49, 63, 81, 93, 127, 147, 189, 217, 243, 279, 343, 381, 441, 567, 651, 729, 837, 889, 961, 1029, 1143, 1323, 1519, 1701, 1953, 2187, 2401, 2511, 2667, 2883, 3087, 3429, 3937, 3969, 4557, 5103, 5859, 6223, 6561, 6727, 7203, 7533, 8001, 8191, 8649, 9261 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..52.

EXAMPLE

63 is included because the prime factorization of 63 is 3^2 * 7 = (2^2 -1)^2 *(2^3 -1).

MAPLE

isA000668 := proc(n)

    if n in [   3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727] then

        true;

    else

        false;

    end if;

end proc:

isA056652 := proc(n)

    local p;

    for p in numtheory[factorset](n) do

        if not isA000668(p) then

            return false;

        end if;

    end do:

    true ;

end proc:

for n from 2 to 1000 do

    if isA056652(n) then

        printf("%d, ", n);

    end if;

end do: # R. J. Mathar, Feb 19 2017

PROG

(PARI) isok(n) = {if (n==1, return (0)); my(f = factor(n)); for (k=1, #f~, if (! ((q=ispower(f[k, 1]+1, , &e)) && isprime(q) && (e==2)), return(0)); ); 1; } \\ Michel Marcus, Apr 25 2016

CROSSREFS

Cf. A000668, A046528.

Sequence in context: A096102 A045797 A118555 * A014959 A057233 A125227

Adjacent sequences:  A056649 A056650 A056651 * A056653 A056654 A056655

KEYWORD

nonn

AUTHOR

Leroy Quet, Aug 09 2000

EXTENSIONS

Offset corrected and more terms by Michel Marcus, Apr 25 2016

STATUS

approved

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Last modified June 25 11:55 EDT 2017. Contains 288710 sequences.