A366811 The number of divisors of prime(n)#+1 where p# is the product of all the primes from 2 to p inclusive.

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

Offset

0,1

Links

Table of n, a(n) for n=0..74.

Formula

a(n) = sigma0(prime(n)#+1) = A000005(A006862(n)).

Example

a(6)=4 because the divisors of 13#+1 = 30031 are {1, 59, 509, 30031}.

Maple

seq(numtheory[tau](mul(ithprime(k), k=1..n)+1), n=0..30);

Mathematica

Map[DivisorSigma[0, #] &, 1 + FoldList[Times, 1, Prime@ Range@ 19] ] (* Michael De Vlieger, Oct 25 2023 *)

Crossrefs

Cf. A006862, A000005, A054988, A366808, A366812, A064145.

Sequence in context: A279611 A008767 A244461 * A343925 A105255 A351023

Adjacent sequences: A366808 A366809 A366810 * A366812 A366813 A366814

Keyword

nonn

Author

Sean A. Irvine, Oct 23 2023

Status

approved