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.
%I A277621 #36 Feb 21 2020 20:21:28
%S A277621 1,1,0,1,0,1,1,1,0,5,3,5,5,13,11,11,11,13,45,105,136,105,165,332,492,
%T A277621 501,482,684,720,1095,1656,3273,3136,3901,4948,6674,7641,15047,12879,
%U A277621 17217,38901,75540,37743,73594,84249,88592,207324,403493,710536,922853,662019
%N A277621 Number of pairs (a,b) such that a*b = n! and d(a) = d(b) with d = A000005 and a <= b.
%H A277621 Project Euler, <a href="https://projecteuler.net/problem=598">Problem 598: Split Divisibilities</a>
%e A277621 For n = 9, there are 5 pairs (a,b): (384,945), (420,864), (480,756), (540,672), (560,648)
%p A277621 a:=proc(n) local S,nf,DD,d,dd:with(numtheory): S:=0:nf:=n!:DD:=divisors(nf):dd:=floor(sqrt(nf)): for d in DD while d <dd do if tau(d)=tau(nf/d) then S:=S +1 end if: end do: S end proc: # only for small n # _Leonid Bedratyuk_, Apr 16 2017
%t A277621 a[n_] := Length@ Select[ Divisors[n!], # <= n!/# && Equal @@ DivisorSigma[0, {#, n!/#}] &]; a /@ Range[0, 20] (* _Giovanni Resta_, Apr 11 2017 *)
%o A277621 (PARI) a(n)=my(c=0); fordiv(n!, a, my(b=n!/a); if(a>b, break); if( numdiv(a) == numdiv(b), c++)); c
%Y A277621 Cf. A000005.
%K A277621 nonn
%O A277621 0,10
%A A277621 _M. Sinan Kul_, Apr 11 2017
%E A277621 a(26)-a(50) from _Giovanni Resta_, Apr 11 2017