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 A260576 Least k such that the product of the first n primes of the form m^2+1 (A002496) divides k^2+1. 0
 1, 3, 13, 327, 36673, 950117, 801495893, 5896798453, 760999599793, 3828797295053127, 520910599208391893, 2418812764637100821917, 793123421312468129647727, 6936392582189824489589830053, 31170731920863007986026123435697, 5284787778858696936313058199017107 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Conjecture: the sequence is infinite. Let b(n) = Product_{k=1..n} A002496(k): 2, 10, 170, 6290, 635290, ... b(1) divides k^2+1 for k = 1, 3, 5, ... b(2) divides k^2+1 for k = 3, 7, 13, 17, 23, 27, 33, 37, 43, 47, 53, 57, 63, 67, 73, 77, 83, ... b(3) divides k^2+1 for k = 13, 47, 123, 157, 183, 217, 293, 327, 353, 387, 463, 497, 523, ... b(4) divides k^2+1 for k = 327, 1067, 2707, 2843, 3447, 3583, 5223, 5963, 6617, 7357, 8997, 9133, 9737, 9873, ... b(5) divides k^2+1 for k = 36673, 38067, 66347, 141087, 217443, 240087, 292183, 314827, 320463, ... LINKS Table of n, a(n) for n=1..16. MAPLE with(numtheory):lst:={2}:nn:=100: for i from 1 to nn do: p:=i^2+1: if isprime(p) then lst:=lst union {p}: else fi: od: pr:=1: for n from 1 to 7 do: pr:=pr*lst[n]:ii:=0: for j from 1 to 10^9 while(ii=0) do: if irem(j^2+1, pr)=0 then ii:=1: printf("%d %d \n", n, j): fi: od: od: CROSSREFS Cf. A002496, A005574. Sequence in context: A113526 A113612 A180654 * A156358 A066266 A092845 Adjacent sequences: A260573 A260574 A260575 * A260577 A260578 A260579 KEYWORD nonn AUTHOR Michel Lagneau, Jul 29 2015 EXTENSIONS a(8)-a(17) from Hiroaki Yamanouchi, Aug 15 2015 STATUS approved

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Last modified December 7 10:48 EST 2023. Contains 367650 sequences. (Running on oeis4.)