%I #22 Sep 03 2022 08:48:03

%S 3512071871,10470856319,11956093919,12283814015,13150303199,

%T 15128703359,15966728855,18063158399,21887083295,22572006479,

%U 23388059519,23836221695,23940514367,25231063319,25638464159,27742047839,28160966735,30070781279,31251542399,35160944399

%N Lucas-Carmichael numbers with 7 prime factors.

%H Daniel Suteu, <a href="/A217003/b217003.txt">Table of n, a(n) for n = 1..7464</a> (first 1000 terms from Donovan Johnson)

%e A006972(1249) = 3512071871 = 7*11*17*23*31*53*71.

%o (PARI) upto(n, k=7) = my(A=vecprod(primes(k+1))\2, 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))), forprime(q = p, sqrtnint(B\m, k), 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 30 2022

%Y Cf. A006972 (Lucas-Carmichael numbers), A216925, A216926, A216927, A217002, A217091.

%K nonn

%O 1,1

%A _Donovan Johnson_, Sep 22 2012