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A066755
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Numbers n such that n^2 + 1 is not divisible by k^2 + 1 for any k in [1,n-1].
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2
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1, 2, 4, 6, 10, 14, 16, 20, 24, 26, 34, 36, 40, 44, 46, 50, 54, 56, 60, 66, 70, 74, 76, 84, 86, 90, 94, 96, 100, 104, 110, 114, 116, 120, 124, 126, 130, 134, 136, 144, 146, 150, 156, 160, 164, 170, 176, 180, 184, 186, 190, 194, 196, 204, 206, 210, 214, 220, 224
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OFFSET
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1,2
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COMMENTS
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If n^2 + 1 is prime, n is in the sequence; i.e., the sequence contains A005574. But so are many other values of n: 34,44,46,50,60,70,76,86,96,...
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LINKS
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MAPLE
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a:= proc(n) option remember; local k; for k from 1+
`if`(n=1, 0, a(n-1)) while ormap(t->
irem(k^2+1, t)=0, [(j^2+1)$j=1..k-1]) do od; k
end:
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MATHEMATICA
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a66743[ n_ ] := Length[ Select[ Range[ 1, n ], IntegerQ[ (n^2+1)/(#^2+1) ]& ] ]; Select[ Range[ 1, 300 ], a66743[ # ]==1& ]
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PROG
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(PARI) { n=0; for (m=1, 10^10, k=1; b=1; t=m^2 + 1; while (k < m - 1, if (t%(k^2 + 1)==0, b=0; break); k++); if (b, write("b066755.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Mar 23 2010
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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