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A268752
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Cubefree numbers n such that n^2 + 1 is prime.
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2
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1, 2, 4, 6, 10, 14, 20, 26, 36, 66, 74, 84, 90, 94, 110, 116, 124, 126, 130, 134, 146, 150, 156, 170, 180, 204, 206, 210, 230, 236, 260, 284, 300, 306, 314, 326, 340, 350, 386, 396, 406, 420, 430, 436, 444, 466, 470, 474, 490, 556, 570, 634, 636, 644, 646, 654
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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a(5) = 10 = 2 * 5 that is cubefree. 10^2 + 1 = 101 which is a prime.
a(6) = 14 = 2 * 7 that is cubefree. 14^2 + 1 = 197 which is a prime.
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MAPLE
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select(t -> isprime(t^2+1) and max(map(f->f[2], ifactors(t)[2]))<=2, [$1..1000]); # Robert Israel, Feb 12 2016
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MATHEMATICA
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Select[Range[1000], FreeQ[FactorInteger[#], {_, k_ /; k > 2}] && PrimeQ[#^2 + 1] &]
Select[Range[1000], Max[FactorInteger[#][[;; , 2]]]<3&&PrimeQ[#^2+1]&] (* Harvey P. Dale, May 30 2023 *)
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PROG
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(PARI) for(n=1, 1000, f = factor(n)[, 2]; if ((#f == 0) || vecmax(f) < 3, if (isprime(n^2+1), print1(n, ", "))));
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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