OFFSET
1,1
COMMENTS
Subsequence of A080747 from which this differs for the first time at n=78, with A080747(78) = 294409, a term not present here.
Is this sequence infinite?
According to Sierpinski there are infinitely many Poulet numbers which are not super-Poulet numbers. But his definition of Poulet numbers includes the even pseudoprimes to base 2 (A006935), and the proof is based on the infinitude of this sequence and that super-Poulet numbers are never even.
REFERENCES
W. Sierpinski, Elementary Theory of Numbers, ed. A. Schinzel, North-Holland Mathematical Library (2nd ed.), Amsterdam: North Holland, 1988, Chapter V, p. 234, Exercise 1.
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Poulet Number
Eric Weisstein's World of Mathematics, Super-Poulet Numbers
Wikipedia, Super-Poulet number
EXAMPLE
561 is in the sequence because 2^561 % 561 == 2 but 33|561 and 2^33 % 33 = 8 <> 2. - David A. Corneth, Feb 28 2019
MATHEMATICA
Select[Select[Range[3, 100000, 2], !PrimeQ[ # ] && PowerMod[2, (# - 1), # ] == 1 &], Union[PowerMod[2, Rest[Divisors[#]], #]] != {2}& ]
PROG
(PARI)
is_A050217(n) = if(isprime(n), 0, fordiv(n, d, if(Mod(2, d)^d!=2, return(0))); (n>1)); \\ After Charles R Greathouse IV's Aug 27 2016 PARI-program in A050217.
is_A306487(n) = (is_A001567(n) && !is_A050217(n)); \\ (Probably could be reduced to a simpler program). - Antti Karttunen, Feb 28 2019
(PARI) is(n) = {if(isprime(n) || n < 2 || n%2 == 0, return(0)); if(Mod(2, n)^n!=2, return(0) , d = divisors(n); for(i = 1, #d-1, if(Mod(2, d[i])^d[i]!=2, return(1) ) ) ); 0 } \\ David A. Corneth, Feb 28 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Feb 18 2019
STATUS
approved