|
%I #13 Aug 29 2022 10:26:22
%S 199195047359,220323712895,259305479279,325451502935,472765412735,
%T 491091874559,498357905759,517270926095,609349053599,769658803199,
%U 832015353455,853833772799,898951575599,962940227039,1087044101759,1122857491679,1249765950719,1297923596255
%N Lucas-Carmichael numbers with 8 prime factors.
%H Daniel Suteu and Donovan Johnson, <a href="/A217091/b217091.txt">Table of n, a(n) for n = 1..5323</a> (terms 1..1000 from Donovan Johnson)
%e A006972(5453) = 199195047359 = 7*11*17*19*23*31*47*239.
%o (PARI) upto(n, k=8) = my(A = vecprod(primes(k)), B=n); (f(m,l,p,k,u=0,v=0) = my(list=List()); if(k==1, forprime(p=u, v, my(t=m*p); if((t+1)%l == 0 && (t+1)%(p+1) == 0, listput(list, t))), my(s = sqrtnint(B\m, k)); forprime(q = p, s, my(t = m*q); my(L=lcm(l,q+1)); if(gcd(L,t) == 1, my(u=ceil(A/t), v=B\t); if(u <= v, my(r=nextprime(q+1)); if(k==2 && r>u, u=r); list=concat(list, f(t, L, r, k-1, u, v)))))); list); vecsort(Vec(f(1, 1, 3, k))); \\ _Daniel Suteu_, Aug 29 2022
%Y Cf. A006972 (Lucas-Carmichael numbers), A216925, A216926, A216927, A217002, A217003.
%K nonn
%O 1,1
%A _Donovan Johnson_, Sep 26 2012
|
