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 A217279 Numbers of the form n^2 + 1 without prime divisors of the form a^2 + 1. 1
 1157, 1937, 2117, 2501, 3601, 4901, 5777, 7397, 9217, 10001, 10817, 12997, 18497, 20737, 26897, 34597, 36101, 37637, 38417, 45797, 48401, 51077, 59537, 60517, 64517, 70757, 75077, 81797, 86437, 87617, 92417, 99857, 102401, 104977, 108901, 111557, 119717 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The corresponding n are in A217276. a(n) == 1, 17, 37, 57, 77, 97 mod 100. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE 1157 is in the sequence because 1157 = 34^2 + 1 = 13*89 and the numbers 13, 89 are not of the form 1 plus a square. MAPLE isA217279 := proc(n) if issqr(n-1) then for d in numtheory[factorset](n) do if issqr(d-1) then return false; end if; end do: return true ; else false; end if; end proc: for n from 1 to 300 do if isA217279(n^2+1) then printf("%d ", n^2+1) ; end if; end do: # R. J. Mathar, Oct 01 2012 MATHEMATICA Select[1 + Range[400]^2, Not[PrimeQ[#]] && Intersection[Divisors[#], 1 + Range[Sqrt[# - 1] - 1]^2] == {} &] (* Alonso del Arte, Sep 29 2012 *) CROSSREFS Cf. A002522, A005574, A217276, A181436, A180252. Sequence in context: A264271 A264089 A264278 * A204478 A031746 A219148 Adjacent sequences: A217276 A217277 A217278 * A217280 A217281 A217282 KEYWORD nonn AUTHOR Michel Lagneau, Sep 29 2012 STATUS approved

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Last modified September 23 12:57 EDT 2023. Contains 365551 sequences. (Running on oeis4.)