cp's OEIS Frontend

A343935 Number of ways to choose a multiset of n divisors of n.

%I A343935 #10 Jul 05 2024 09:31:50
%S A343935 1,3,4,15,6,84,8,165,55,286,12,6188,14,680,816,4845,18,33649,20,53130,
%T A343935 2024,2300,24,2629575,351,3654,4060,237336,30,10295472,32,435897,7140,
%U A343935 7770,8436,177232627,38,10660,11480,62891499,42,85900584,44,1906884,2118760
%N A343935 Number of ways to choose a multiset of n divisors of n.
%F A343935 a(n) = ((sigma(n), n)) = binomial(sigma(n) + n - 1, n) where sigma = A000005 and binomial = A007318.
%e A343935 The a(1) = 1 through a(5) = 6 multisets:
%e A343935   {1}  {1,1}  {1,1,1}  {1,1,1,1}  {1,1,1,1,1}
%e A343935        {1,2}  {1,1,3}  {1,1,1,2}  {1,1,1,1,5}
%e A343935        {2,2}  {1,3,3}  {1,1,1,4}  {1,1,1,5,5}
%e A343935               {3,3,3}  {1,1,2,2}  {1,1,5,5,5}
%e A343935                        {1,1,2,4}  {1,5,5,5,5}
%e A343935                        {1,1,4,4}  {5,5,5,5,5}
%e A343935                        {1,2,2,2}
%e A343935                        {1,2,2,4}
%e A343935                        {1,2,4,4}
%e A343935                        {1,4,4,4}
%e A343935                        {2,2,2,2}
%e A343935                        {2,2,2,4}
%e A343935                        {2,2,4,4}
%e A343935                        {2,4,4,4}
%e A343935                        {4,4,4,4}
%t A343935 multchoo[n_,k_]:=Binomial[n+k-1,k];
%t A343935 Table[multchoo[DivisorSigma[0,n],n],{n,25}]
%o A343935 (Python)
%o A343935 from math import comb
%o A343935 from sympy import divisor_count
%o A343935 def A343935(n): return comb(divisor_count(n)+n-1,n) # _Chai Wah Wu_, Jul 05 2024
%Y A343935 Diagonal n = k of A343658.
%Y A343935 Choosing n divisors of n - 1 gives A343936.
%Y A343935 The version for chains of divisors is A343939.
%Y A343935 A000005 counts divisors.
%Y A343935 A000312 = n^n.
%Y A343935 A007318 counts k-sets of elements of {1..n}.
%Y A343935 A009998 = n^k (as an array, offset 1).
%Y A343935 A059481 counts k-multisets of elements of {1..n}.
%Y A343935 A146291 counts divisors of n with k prime factors (with multiplicity).
%Y A343935 A253249 counts nonempty chains of divisors of n.
%Y A343935 Strict chains of divisors:
%Y A343935 - A067824 counts strict chains of divisors starting with n.
%Y A343935 - A074206 counts strict chains of divisors from n to 1.
%Y A343935 - A251683 counts strict length k + 1 chains of divisors from n to 1.
%Y A343935 - A334996 counts strict length-k chains of divisors from n to 1.
%Y A343935 - A337255 counts strict length-k chains of divisors starting with n.
%Y A343935 - A337256 counts strict chains of divisors of n.
%Y A343935 - A343662 counts strict length-k chains of divisors.
%Y A343935 Cf. A062319, A143773, A163767, A176029, A327527, A334997, A343661.
%K A343935 nonn
%O A343935 1,2
%A A343935 _Gus Wiseman_, May 05 2021