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 A056652 Integers > 1 whose prime divisors are all Mersenne primes (i.e., of the form (2^p - 1)). 5
 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 Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..471 from Michael De Vlieger) FORMULA Sum_{n>=1} 1/a(n) = - 1 + Product_{p in A000668} p/(p-1) = 0.82292512097260346512... - Amiram Eldar, Sep 27 2020 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 MATHEMATICA Block[{nn = 10^4, s}, s = TakeWhile[Select[2^Prime@ Range@ 8 - 1, PrimeQ], # <= nn &]; Select[Range@ nn, AllTrue[FactorInteger[#][[All, 1]], MemberQ[s, #] &] &]] (* Michael De Vlieger, Sep 03 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: A316157 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 added by Michel Marcus, Apr 25 2016 STATUS approved

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Last modified October 22 10:18 EDT 2020. Contains 337950 sequences. (Running on oeis4.)