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 A050217 Super-Poulet numbers: Poulet numbers whose divisors d all satisfy d|2^d-2. 7
 341, 1387, 2047, 2701, 3277, 4033, 4369, 4681, 5461, 7957, 8321, 10261, 13747, 14491, 15709, 18721, 19951, 23377, 31417, 31609, 31621, 35333, 42799, 49141, 49981, 60701, 60787, 65077, 65281, 80581, 83333, 85489, 88357, 90751 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Every semiprime in A001567 is in this sequence (see Sierpiński). a(61) = 294409 is the first term having more than two prime factors. See A178997 for super-Poulet numbers having more than two prime factors. - T. D. Noe, Jan 11 2011 Composite numbers n such that 2^d == 2 (mod n) for every d|n. - Thomas Ordowski, Sep 04 2016 Composite numbers n such that 2^p == 2 (mod n) for every prime p|n. - Thomas Ordowski, Sep 06 2016 Composite numbers n = p(1)^e(1)*p(2)^e(2)*...*p(k)^e(k) such that 2^gcd(p(1)-1,p(2)-1,...,p(k)-1) == 1 (mod n). - Thomas Ordowski, Sep 12 2016 Nonsquarefree terms are divisible by the square of a Wieferich prime (see A001220). These include 1194649, 12327121, 5654273717, 26092328809, 129816911251. - Robert Israel, Sep 13 2016 Composite numbers n such that 2^A258409(n) == 1 (mod n). - Thomas Ordowski, Sep 15 2016 REFERENCES W. Sierpiński, Elementary Theory of Numbers, Warszawa, 1964, p. 231. LINKS T. D. Noe, Table of n, a(n) for n = 1..1000 Eric Weisstein's World of Mathematics, Super-Poulet Numbers Wikipedia, Super-Poulet number MAPLE filter:= = proc(n)     not isprime(n) and andmap(p -> 2&^p mod n = 2, numtheory:-factorset(n)) end proc: select(filter, [seq(i, i=3..10^5, 2)]); # Robert Israel, Sep 13 2016 MATHEMATICA Select[Range[1, 110000, 2], !PrimeQ[#] && Union[PowerMod[2, Rest[Divisors[#]], #]] == {2} & ] PROG (PARI) is(n)=if(isprime(n), return(0)); fordiv(n, d, if(Mod(2, d)^d!=2, return(0))); n>1 \\ Charles R Greathouse IV, Aug 27 2016 CROSSREFS A214305 is a subsequence. A065341 is a subsequence. - Thomas Ordowski, Nov 20 2016 Cf. A001220, A001567, A178997. Sequence in context: A068216 A038473 A276733 * A214305 A086837 A020230 Adjacent sequences:  A050214 A050215 A050216 * A050218 A050219 A050220 KEYWORD nonn AUTHOR STATUS approved

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