cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A278973 #14 Jun 22 2022 14:49:33
%S A278973 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,
%T A278973 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,
%U A278973 48,8,2,1728,8,8,32,8,128,8,128,16,24,64,8,24,16,16
%N A278973 Number of divisors of the n-th Bell number (A000110(n)).
%H A278973 Amiram Eldar, <a href="/A278973/b278973.txt">Table of n, a(n) for n = 0..104</a>
%F A278973 a(n) = tau(A000110(n)).
%F A278973 a(n) = A000005(A000110(n)).
%e A278973 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.
%e A278973 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.
%t A278973 DivisorSigma[0,BellB[Range[0,70]]] (* _Harvey P. Dale_, Mar 04 2019 *)
%o A278973 (Python)
%o A278973 from sympy import bell, divisor_count
%o A278973 def A278973(n): return divisor_count(bell(n)) # _Chai Wah Wu_, Jun 22 2022
%Y A278973 Cf. A000005, A000110.
%K A278973 nonn
%O A278973 0,3
%A A278973 _Jon E. Schoenfield_, Dec 02 2016