A257643 Carmichael numbers n such that n-1 is squarefree.

139952671, 74689102411, 121254376891, 187054437571, 231440115271, 236359158267, 303008129971, 306252926071, 380574791611, 426951670531, 556303918171, 639109148371, 660950414671, 1101375141511, 1483826843731, 1487491483171, 1861175569891, 2794268624071

Offset

1,1

Comments

If n is a Carmichael number with n-1 squarefree, then gcd(phi(n),n-1) = lambda(n); i.e. Carmichael lambda function A002322.

Links

Robert Israel and Charles R Greathouse IV, Table of n, a(n) for n = 1..1037 (first 164 terms from Israel)

Prog

(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)
is(n) = n%2 && !isprime(n) && t(n) && n>1 \\ Charles R Greathouse IV, Nov 09 2015

Crossrefs

Subsequence of A185321.

Cf. A002997, A264012, A007674.

Sequence in context: A109093 A217002 A036744 * A262532 A075130 A202280

Adjacent sequences: A257640 A257641 A257642 * A257644 A257645 A257646

Keyword

nonn

Author

Thomas Ordowski, Nov 05 2015

Status

approved