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A253595
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Least Carmichael number that is divisible by the n-th cyclic number A003277(n), or 0 if no such number exists.
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2
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561, 1105, 1729, 561, 1105, 62745, 561, 1729, 6601, 2465, 2821, 561, 825265, 29341, 6601, 334153, 62745, 561, 2433601, 74165065, 29341, 1105, 8911, 116150434401, 10024561, 10585, 41041, 2508013, 55462177, 1105, 11921001
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OFFSET
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3,1
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COMMENTS
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Has any odd cyclic number at least one Carmichael multiple?
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 3..2747 (calculated using data from Claude Goutier; terms 3..291 from Tim Johannes Ohrtmann, terms 292..853 from Max Alekseyev)
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EXAMPLE
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a(8) = 62745 because this is the least Carmichael number which is divisible by 15 (the 8th cyclic number).
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PROG
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(PARI) Korselt(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1
isA002997(n)=n%2 && !isprime(n) && Korselt(n) && n>1
a(n) = {on = odd cyclic number(n); cn = 1; until (isA002997(cn) && (cn % on == 0), cn++); cn; }
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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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