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A257643
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Carmichael numbers k such that k-1 is squarefree.
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2
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139952671, 74689102411, 121254376891, 187054437571, 231440115271, 236359158267, 303008129971, 306252926071, 380574791611, 426951670531, 556303918171, 639109148371, 660950414671, 1101375141511, 1483826843731, 1487491483171, 1861175569891, 2794268624071
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OFFSET
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1,1
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COMMENTS
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If k is a Carmichael number with k-1 squarefree, then gcd(phi(k),k-1) = lambda(k), i.e., Carmichael lambda function A002322.
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LINKS
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Amiram Eldar, Table of n, a(n) for n = 1..5287 (terms below 10^22, calculated using data from Claude Goutier; terms 1..164 from Robert Israel, terms 165..1037 from Charles R Greathouse IV)
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PROG
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(PARI) t(n) = my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1;
is(n) = n%2 && !isprime(n) && t(n) && n>1;
isok(n) = is(n) && issquarefree(n-1); \\ Altug Alkan, Nov 06 2015
(PARI) is(n) = my(f=factor(n)); for(i=1, #f~, if(f[i, 1]%4<3 || f[i, 2]>1 || (n-1)%(f[i, 1]-1), return(0))); !isprime(n) && issquarefree(n-1)
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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