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

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

Offset: 1

Author

Thomas Ordowski, Nov 05 2015

Keywords

• nonn

Comments

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

Links

• 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)
• Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.

Crossrefs

Subsequence of A185321.

Cf. A002997, A264012, A007674.

Programs

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