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 A180342 a(n) = the smallest number k such that the smallest prime factor of k^2 + 1 equals A002144(n). 0
 2, 34, 4, 46, 6, 50, 76, 194, 100, 144, 366, 10, 730, 324, 374, 254, 286, 266, 886, 274, 14, 794, 610, 546, 16, 456, 494, 334, 724, 964, 520, 526, 834, 664, 1596, 504, 3510, 20, 2720, 1234, 1120, 516, 566, 874, 810, 756, 1134, 2110, 1224, 24, 670, 726 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The sequence giving the smallest number k such that the greatest prime factor of k^2 + 1 equals A002144(n) is A002314. LINKS Table of n, a(n) for n=1..52. EXAMPLE a(1) = 2 because 2^2 + 1 = 5 = A002144(1) ; a(2) = 34 because 34^2 + 1= 13*89 = A002144(2) * 89 ; a(3) = 4 because 4^2 + 1 = 17 = A002144(3) ; a(4) = 46 because 46^2 + 1 = 29*73 = A002144(4) * 73. MAPLE with(numtheory):T:=array(1..200):k:=1:for p from 1 to 1000 do: if type(p, prime)=true and irem(p, 4)=1 then T[k]:=p:k:=k+1:else fi:od:for q from 1 to k do:z:=T[q]:ind:=0:for n from 1 to 10000 while(ind=0) do: x:=n^2+1:y:=factorset(x):if z=y[1] then ind:=1:printf(`%d, `, n):else fi:od: od: CROSSREFS Cf. A002522, A002144, and A002314. Sequence in context: A003820 A112980 A109336 * A343905 A232591 A098869 Adjacent sequences: A180339 A180340 A180341 * A180343 A180344 A180345 KEYWORD nonn AUTHOR Michel Lagneau, Jan 18 2011 STATUS approved

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Last modified May 18 16:58 EDT 2024. Contains 372664 sequences. (Running on oeis4.)