A340092 - OEIS

%I #14 Apr 22 2024 14:28:13

%S 1729,2821,15841,29341,41041,52633,63973,75361,101101,115921,126217,

%T 172081,188461,252601,278545,294409,314821,334153,340561,399001,

%U 488881,512461,530881,552721,656601,658801,670033,748657,825265,838201,852841,997633,1024651,1033669,1050985,1082809,1152271,1193221,1461241,1569457

%N Carmichael numbers k for which A053575(k) [the odd part of phi] does not divide k-1.

%H Amiram Eldar, <a href="/A340092/b340092.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.

%t odd[n_] := n/2^IntegerExponent[n, 2]; Select[Range[1, 10^6, 2], CompositeQ[#] && Divisible[# - 1, CarmichaelLambda[#]] && !Divisible[# - 1, odd @ EulerPhi[#]] &] (* _Amiram Eldar_, Dec 31 2020 *)

%o (PARI)

%o A000265(n) = (n>>valuation(n, 2));

%o A002322(n) = lcm(znstar(n)[2]);

%o isA340092(n) = ((n>1)&&!isprime(n)&&(!((n-1)%A002322(n)))&&(0<((n-1)%A000265(eulerphi(n)))));

%Y Complement of A339869 in A002997.

%Y Subsequence of A340091.

%Y Cf. A002322, A053575.

%K nonn

%O 1,1

%A _Antti Karttunen_, Dec 31 2020