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A258839
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Carmichael numbers whose prime factors all have the form p=1+x^2+y^2 for some x,y in Z.
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1
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561, 162401, 410041, 488881, 656601, 2433601, 36765901, 109393201, 171454321, 176659201, 178837201, 189941761, 221884001, 288120421, 600892993, 618068881, 721244161, 931694401, 985052881, 1183104001, 1828377001, 1848112761, 1943951041, 2361232477, 2438403661
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OFFSET
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1,1
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COMMENTS
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Banks & Freiberg show that this sequence is infinite.
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LINKS
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PROG
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(PARI) has(n)=for(x=sqrtint(n\2), sqrtint(n-1), if(issquare(n-x^2-1), return(1))); 0
Korselt(n, f=factor(n))=for(i=1, #f~, if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1
is(n)=my(f); if(n%2==0||isprime(n)||!Korselt(n, f=factor(n))||n<9, return(0)); for(i=1, #f~, if(!has(f[i, 1]), return(0))); 1 \\ Charles R Greathouse IV, Jun 12 2015
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CROSSREFS
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Cf. A002997 (Carmichael numbers), A079545 (primes of the form x^2 + y^2 + 1).
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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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