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 A179768 Semiprimes of form p*q with p < q, such that 2^p - 1 == 0 (mod q). 1
 6, 21, 155, 253, 889, 979, 1081, 6757, 8251, 13861, 18533, 31987, 32047, 34453, 60581, 64261, 73153, 106483, 110497, 114481, 126253, 212111, 212273, 256507, 258121, 325967, 337133, 351541, 371953, 383183, 392941, 417917, 457207, 482653, 548047, 869221, 933661, 946051 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Number of terms < 10^k: 1, 2, 6, 9, 17, 38, 91, 222, ..., . LINKS Robert Israel, Table of n, a(n) for n = 1..518 EXAMPLE 6 is a term because 6=2*3 and 2^2-1 (mod 3)=0; 21 is a term because 21=3*7 and 2^3-1 (mod 7)=0; 155 is a term because 155=5*31 and 2^5-1 (mod 31)=0; 253 is a term because 253=11*23 and 2^11-1 (mod 23)=0; 889 is a term because 889=7*127 and 2^7-1 (mod 127)=0; 979 is a term because 979=11*89 and 2^11-1 (mod 89)=0; etc. MAPLE N:= 10^6: # to get all terms <= N Q:= ceil(fsolve(q*log[2](q)=N)); Res:= NULL: q:= 2: do q:= nextprime(q); if q > Q then break fi; p:= numtheory:-order(2, q); if not isprime(p) then next fi; v:= p*q; if v <= N then Res:= Res, v fi od: sort([Res]); # Robert Israel, Nov 23 2019 MATHEMATICA fQ[n_] := Block[{fi = FactorInteger@ n}, Plus @@ Last /@ fi == 2 && PowerMod[2, fi[[1, 1]], fi[[2, 1]]] == 1]; Select[ Range@ 1000000, fQ] (* Robert G. Wilson v, Jan 10 2011 *) CROSSREFS Cf. A000079, A001358. Sequence in context: A054366 A304264 A210443 * A131960 A244299 A143049 Adjacent sequences: A179765 A179766 A179767 * A179769 A179770 A179771 KEYWORD nonn AUTHOR Juri-Stepan Gerasimov, Jan 10 2011 EXTENSIONS Corrected, extended & edited by Robert G. Wilson v, Jan 10 2011 STATUS approved

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Last modified December 7 14:31 EST 2022. Contains 358656 sequences. (Running on oeis4.)