A278973 Number of divisors of the n-th Bell number (A000110(n)).

1, 1, 2, 2, 4, 6, 4, 2, 36, 16, 6, 16, 8, 2, 8, 8, 4, 30, 8, 12, 36, 16, 64, 16, 8, 64, 32, 64, 16, 48, 64, 4, 24, 4, 16, 96, 16, 8, 16, 8, 8, 48, 2, 128, 48, 32, 16, 128, 16, 4, 32, 8, 24, 48, 8, 2, 1728, 8, 8, 32, 8, 128, 8, 128, 16, 24, 64, 8, 24, 16, 16

Offset: 0

Author

Jon E. Schoenfield, Dec 02 2016

Keywords

• nonn

Examples

			Bell(17) = A000110(17) = 82864869804 = 2^2 * 3^4 * 255755771^1; exponents are 2, 4, 1, so its number of divisors is (2+1)*(4+1)*(1+1) = 3*5*2 = 30; thus a(17) = 30.
Bell(56) = A000110(56) = 6775685320645824322581483068371419745979053216268760300 = 2^2 * 3*2 * 5^2 * 7^1 * 43^1 * 481531^1 * 5134193^1 * 206802391^1 * 48920650786823172374961445939^1; exponents are 2, 2, 2, 1, 1, 1, 1, 1, 1, so its number of divisors is (2+1)^3 * (1+1)^6 = 1728; thus a(56) = 1728.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..104

Crossrefs

Cf. A000005, A000110.

Programs

Mathematica

DivisorSigma[0,BellB[Range[0,70]]] (* Harvey P. Dale, Mar 04 2019 *)

Python

from sympy import bell, divisor_count
def A278973(n): return divisor_count(bell(n)) # Chai Wah Wu, Jun 22 2022

Formula

a(n) = tau(A000110(n)).

a(n) = A000005(A000110(n)).