A366808 The number of divisors of prime(n)#-1 where p# is the product of all the primes from 2 to p inclusive.

1, 2, 2, 4, 2, 2, 4, 8, 8, 4, 4, 16, 2, 4, 8, 8, 4, 8, 8, 4, 4, 16, 8, 2, 4, 4, 16, 16, 16, 8, 8, 8, 8, 8, 8, 16, 16, 16, 32, 8, 32, 16, 32, 16, 16, 16, 16, 4, 8, 8, 4, 16, 8, 16, 4, 16, 16, 128, 16, 8, 8, 16, 16, 8, 8, 2, 8, 2, 16, 8, 32, 32, 16, 16, 64, 32

Offset: 1

Author

Sean A. Irvine, Oct 23 2023

Keywords

• nonn

Examples

			a(4)=4 because the divisors of 7#-1 = 209 are {1, 11, 19, 209}.
		

Crossrefs

Cf. A057588, A000005, A054989, A366809, A064145.

Programs

Maple

seq(numtheory[tau](mul(ithprime(k), k=1..n)-1), n=1..30);

Mathematica

Map[DivisorSigma[0, #] &, -1 + FoldList[Times, Prime@ Range@ 30] ] (* Michael De Vlieger, Oct 25 2023 *)

Formula

a(n) = sigma0(prime(n)#-1) = A000005(A057588(n)).