|
%I #9 Sep 21 2015 20:38:15
%S 165,231,273,357,399,598,715,935,1015,1105,1547,1595,1885,1886,2015,
%T 2093,2387,2397,2451,2465,2585,2679,2737,2821,2915,3059,3445,3913,
%U 3965,4123,4991,5015,5467,5719,6097,6545,7055,7189,7285,7553,7843,8555,8569,8715,8855
%N Quasi-Carmichael numbers to at least one positive base.
%H Tim Johannes Ohrtmann, <a href="/A259283/b259283.txt">Table of n, a(n) for n = 1..2963</a>
%e a(1) = 165 because this is the first squarefree composite number n such that at least one positive integer b except 0 exists such that for every prime factor p of n applies that p+b divides n+b (3): 165=3*5*11 and 6, 8, 14 all divide 168.
%o (PARI) for(n=2, 1000000, if(!isprime(n), if(issquarefree(n), f=factor(n); b=0; until(c==0 || b==n, b++; c=0; for(i=1, #f[, 1], if((n+b)%(f[i, 1]+b)>0, c++)); if(c==0, print1(n, ", "))))))
%Y Cf. A257750, A257759, A259282.
%K nonn
%O 1,1
%A _Tim Johannes Ohrtmann_, Jun 23 2015
|
