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
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)
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
KEYWORD
nonn
AUTHOR
STATUS
approved