A217091 Lucas-Carmichael numbers with 8 prime factors.

199195047359, 220323712895, 259305479279, 325451502935, 472765412735, 491091874559, 498357905759, 517270926095, 609349053599, 769658803199, 832015353455, 853833772799, 898951575599, 962940227039, 1087044101759, 1122857491679, 1249765950719, 1297923596255

Offset: 1

Author

Donovan Johnson, Sep 26 2012

Keywords

• nonn

Examples

			A006972(5453) = 199195047359 = 7*11*17*19*23*31*47*239.
		

Links

• Daniel Suteu and Donovan Johnson, Table of n, a(n) for n = 1..5323 (terms 1..1000 from Donovan Johnson)

Crossrefs

Cf. A006972 (Lucas-Carmichael numbers), A216925, A216926, A216927, A217002, A217003.

Programs

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