|
| |
|
|
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
|
| |
|
|
