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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 MATHEMATICA filterQ[n_] := CompositeQ[n] && AllTrue[Divisors[n], PowerMod[2, #, n] == PowerMod[2, n/#, n]&]; Select[Range[1, 10^6, 2], filterQ] (* Jean-François Alcover, Jun 18 2020 *) 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 May 8 12:48 EDT 2021. Contains 343666 sequences. (Running on oeis4.)