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 A256011 Integers n with the property that the largest prime factor of n^2+1 is less than n. 5
 7, 18, 21, 38, 41, 43, 47, 57, 68, 70, 72, 73, 83, 99, 111, 117, 119, 123, 128, 132, 133, 142, 157, 172, 173, 174, 182, 185, 191, 192, 193, 200, 211, 212, 216, 233, 237, 239, 242, 251, 253, 255, 265, 268, 273, 278, 293, 294, 302, 305, 307, 313, 319, 322, 327 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Every Pythagorean prime, p, can be written as the sum of two positive integers, a and b, such that ab is congruent to 1 (mod p).  Further: no number is the addend of two different primes, and the numbers that are NEVER addends are precisely the numbers in this list. In particular: 5 = 2+3 and (2)(3) = 6 == 1 mod 5, 13 = 5+8 and (5)(8) = 40 == 1 mod 13, 17 = 4+13 and (4)(13) = 52 == 1 mod 17, 29 = 12+17 and (12)(17) = 204 == 1 mod 29, and so on. LINKS Giovanni Resta, Table of n, a(n) for n = 1..10000 EXAMPLE 7^2+1 = 50 = 2 * 5^2; 18^2+1 = 325 = 5^2 * 13; 21^2+1 = 442 = 2 * 13 * 17. MAPLE select(n -> max(numtheory:-factorset(n^2+1))

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Last modified May 21 15:12 EDT 2019. Contains 323444 sequences. (Running on oeis4.)