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A278973
Number of divisors of the n-th Bell number (A000110(n)).
1
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
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
Sequence in context: A051495 A368157 A286542 * A073256 A166362 A050469
KEYWORD
nonn
AUTHOR
Jon E. Schoenfield, Dec 02 2016
STATUS
approved