A023516 Number of distinct prime divisors of prime(n)*prime(n-1) - 1.

0, 1, 2, 2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 3, 4, 3, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 4, 3, 2, 4, 2, 3, 2, 4, 3, 3, 4, 3, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 4, 2, 3, 3, 4, 4, 4, 4, 4, 3, 4, 2, 3, 4, 2, 4, 4, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 2, 4

Offset: 1

Author

Clark Kimberling

Keywords

• nonn

Comments

This is taking prime(0)=1 (see first comment in A023515). - Vincenzo Librandi, Apr 27 2019

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A023515, A023524, A023568, A023575, A023582, A023589.

Programs

Magma

[#PrimeDivisors(NthPrime(n)*(NthPrime(n-1))-1): n in [1..100]]; // Vincenzo Librandi, Apr 27 2019

Maple

0,seq(nops(numtheory:-factorset(ithprime(n)*ithprime(n-1)-1)),n=2..120); # Muniru A Asiru, Apr 29 2019

Mathematica

Prepend[Table[PrimeNu[Prime[n] Prime[n-1] - 1], {n, 2, 80}],0] (* Vincenzo Librandi, Apr 27 2019 *)

PARI

a(n) = if (n==1, 0, omega(prime(n)*prime(n-1) - 1)); \\ Michel Marcus, Apr 30 2019

Formula

a(n) = A001221(A023515(n)).