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 A260868 Numbers for which the least k > 1 which divides n + 2^k - 2 is different from the smallest prime factor of n. 1

%I

%S 89,173,179,229,269,439,499,509,523,557,577,599,619,677,719,769,797,

%T 839,859,929,1009,1013,1031,1049,1061,1069,1109,1129,1217,1223,1237,

%U 1259,1279,1291,1303,1319,1447,1471,1483,1489,1499,1523,1559,1579,1601,1609,1667,1699,1709,1721,1783,1789,1811,1879,1889,1931,1933

%N Numbers for which the least k > 1 which divides n + 2^k - 2 is different from the smallest prime factor of n.

%C Somewhat astonishingly, n = 89 is the only number below 173 for which the least prime factor is different from the least k > 1 which divides n + 2^k - 2. For larger n, this property becomes more frequent.

%C The first composite number in this sequence is a(105) = 3239.

%o (PARI) my(aa(n)=for(k=2,9e9,Mod(2,k)^k+n-2||return(k)));for(n=2,1e5,aa(n)!=factor(n)[1,1]&&print1(n","))

%K nonn

%O 1,1

%A _M. F. Hasler_, Aug 11 2015

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Last modified April 6 22:23 EDT 2020. Contains 333291 sequences. (Running on oeis4.)