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A291601 Composite integers n such that 2^d == 2^(n/d) (mod n) for all d|n. 3
341, 1105, 1387, 2047, 2701, 3277, 4033, 4369, 4681, 5461, 7957, 8321, 10261, 13747, 13981, 14491, 15709, 18721, 19951, 23377, 31417, 31609, 31621, 35333, 42799, 49141, 49981, 60701, 60787, 65077, 65281, 68101, 80581, 83333, 85489, 88357, 90751, 104653, 123251, 129889 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Such n must be odd.

For d=1, we have 2^n == 2 (mod n), implying that n is a Fermat pseudoprime (A001567).

Every Super-Poulet number belongs to this sequence.

LINKS

Robert Israel, Table of n, a(n) for n = 1..1000

MAPLE

filter:= proc(n) local D, d;

  if isprime(n) then return false fi;

  D:= sort(convert(numtheory:-divisors(n), list));

  for d in D while d^2 < n do

    if 2 &^ d - 2 &^(n/d) mod n <> 0 then return false fi

  od:

  true

end proc:

select(filter, [seq(i, i=3..2*10^5, 2)]); # Robert Israel, Aug 28 2017

CROSSREFS

Subsequence of A001567.

Supersequence of A050217, their set difference is given by A291602.

Sequence in context: A087835 A271221 A066488 * A083876 A068216 A038473

Adjacent sequences:  A291598 A291599 A291600 * A291602 A291603 A291604

KEYWORD

nonn

AUTHOR

Max Alekseyev, Aug 27 2017

STATUS

approved

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Last modified December 6 16:24 EST 2019. Contains 329808 sequences. (Running on oeis4.)