A263403 Carmichael numbers k such that the odd part of k-1 is squarefree.

561, 1105, 2465, 2821, 62745, 75361, 278545, 530881, 3224065, 3581761, 4335241, 6049681, 7519441, 8355841, 9582145, 9890881, 10837321, 13696033, 17098369, 19384289, 22665505, 23382529, 26932081, 34657141, 36121345, 37167361, 40280065, 41471521, 43286881

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

Cf. A000265, A002997, A005117.

Sequence in context: A367320 A300629 A135720 * A083733 A339869 A375875

Adjacent sequences: A263400 A263401 A263402 * A263404 A263405 A263406

Keyword

nonn

Author

Thomas Ordowski, Oct 17 2015

Extensions

More terms from Altug Alkan, Oct 17 2015

Status

approved