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

89, 173, 179, 229, 269, 439, 499, 509, 523, 557, 577, 599, 619, 677, 719, 769, 797, 839, 859, 929, 1009, 1013, 1031, 1049, 1061, 1069, 1109, 1129, 1217, 1223, 1237, 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

Offset: 1

Author

M. F. Hasler, Aug 11 2015

Keywords

• nonn

Comments

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.

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

Programs

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","))