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A258839 Carmichael numbers whose prime factors all have the form p=1+x^2+y^2 for some x,y in Z. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Banks & Freiberg show that this sequence is infinite.

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..733 (terms < 10^16, from R. G. E. Pinch data)

William D. Banks, Tristan Freiberg, Carmichael numbers and the sieve, arXiv:1506.03497 [math.NT], 2015.

PROG

(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

CROSSREFS

Cf. A002997 (Carmichael numbers), A079545 (primes of the form x^2 + y^2 + 1).

Sequence in context: A258801 A097061 A290497 * A213867 A139089 A202562

Adjacent sequences:  A258836 A258837 A258838 * A258840 A258841 A258842

KEYWORD

nonn

AUTHOR

Michel Marcus, Jun 12 2015

STATUS

approved

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Last modified April 22 10:22 EDT 2019. Contains 322330 sequences. (Running on oeis4.)