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

0,3

Links

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

Formula

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

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000005, A000110.

Sequence in context: A051495 A368157 A286542 * A073256 A166362 A050469

Adjacent sequences: A278970 A278971 A278972 * A278974 A278975 A278976

Keyword

nonn

Author

Jon E. Schoenfield, Dec 02 2016

Status

approved