OFFSET
1,1
COMMENTS
Are there Carmichael numbers k such that the odd part of k-1 is a Carmichael number?
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
a(1) = 561 because 561 is the first Carmichael number and the odd part of 560 is 35, which is squarefree.
MATHEMATICA
lim = 10^7; f[n_] := NestWhile[#/2 &, n, EvenQ]; t = Cases[Range[1, lim, 2], n_ /; Mod[n, CarmichaelLambda@ n] == 1 && ! PrimeQ@ n]; Select[t, SquareFreeQ@ f[# - 1] &] (* Michael De Vlieger, Oct 19 2015, after Artur Jasinski at A002997 *)
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;
isC(n)=n%2 && !isprime(n) && t(n) && n>1;
is(n)=isC(n) && issquarefree((n-1) >> valuation((n-1), 2));
for(n=1, 1e10, if( is(n), print1(n", "))); \\ Altug Alkan, Oct 17 2015; edited by Michel Marcus, Jun 25 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Ordowski, Oct 17 2015
EXTENSIONS
More terms from Altug Alkan, Oct 17 2015
STATUS
approved