OFFSET
1,1
COMMENTS
EXAMPLE
For 341 = 11 * 31 that is a super-Poulet:
2^11 (mod 31) = 2^31 (mod 11) = 2, hence 341 is a term;
For 525 = 3 * 5^2 * 7 = 15 * 35 = 21 * 25:
2^15 (mod 35) = 2^35 (mod 15) = 8, but
2^21 (mod 25) = 2^25 (mod 21) = 2, hence, 525 is a term.
MAPLE
test := proc(n) local d, q; if n::odd then for d in NumberTheory:-Divisors(n)
do q := iquo(n, d); if q > d and 2 &^ d mod q = 2 and 2 &^ q mod d = 2 then return true fi od fi; false end: select(test, [$(1..10000)]); # Peter Luschny, Sep 17 2020
MATHEMATICA
okQ[x_, y_] := PowerMod[2, x, y] == PowerMod[2, y, x] == 2 && !PrimeQ[Sqrt[x*y]];
nn = 20000;
Union[Reap[Do[If[x*y < nn && okQ[x, y], Sow[x*y]], {x, 1, nn/3, 2}, {y, x, nn/3, 2}]][[2, 1]]] (* Jean-François Alcover, Sep 29 2024, after Harvey P. Dale in A176970 *)
PROG
(PARI) isok(n) = {if ((n % 2), fordiv(n, d, if ((d > n/d) && (lift(Mod(2, d)^(n/d)) == 2) && (lift(Mod(2, n/d)^d) == 2), return(1)); ); ); } \\ Michel Marcus, Sep 17 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Sep 16 2020
EXTENSIONS
More terms from Amiram Eldar, Sep 16 2020
STATUS
approved