A216929 Number of Lucas-Carmichael numbers less than 10^n.

0, 0, 2, 8, 26, 60, 135, 323, 791, 1840, 4216, 9967, 23070, 54356, 129125

Offset: 1

Author

Tim Johannes Ohrtmann, Sep 20 2012

Keywords

• nonn
• more

Crossrefs

Cf. A006972 (Lucas-Carmichael numbers).

Programs

PARI

lucas_carmichael(A, B, k) = A=max(A, vecprod(primes(k+1))\2); (f(m, l, lo, k) = my(list=List()); my(hi=min(sqrtint(B+1)-1, sqrtnint(B\m, k))); if(lo > hi, return(list)); if(k==1, lo=max(lo, ceil(A/m)); my(t=lift(-1/Mod(m,l))); while(t < lo, t += l); forstep(p=t, hi, l, if(isprime(p), my(n=m*p); if((n+1)%(p+1) == 0, listput(list, n)))), forprime(p=lo, hi, if(gcd(m, p+1) == 1, list=concat(list, f(m*p, lcm(l, p+1), p+1, k-1))))); list); f(1, 1, 3, k);
a(n) = my(N=10^n); my(count=0); for(k=3, oo, if(vecprod(primes(k+1))\2 > N, break); count += #lucas_carmichael(1, N, k)); count; \\ Daniel Suteu, Dec 01 2023

Extensions

a(9)-a(11) from Donovan Johnson, Sep 22 2012

a(12) from Donovan Johnson, Sep 26 2012

a(13)-a(15) from Daniel Suteu, Dec 01 2023