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 A379742 #21 Jan 16 2025 02:39:10
%S A379742 1,1,2,6,18,72,234,1088,3600,10416,28080,124080,387828,1921024,
%T A379742 6926400,20941344,54934880,251328000,810152280,4254092800,15266200950,
%U A379742 46208448000,129674387920,640501862400,2197261252368,6404827161600,17436935577600,43314231340800,101062601640000,436914124416000,1355859833328000,7074064925491200
%N A379742 a(n) is the number of divisors of A000178(n).
%H A379742 Paolo Xausa, <a href="/A379742/b379742.txt">Table of n, a(n) for n = 0..1000</a>
%F A379742 a(n) = A000005(A000178(n)).
%F A379742 a(n) = Product_{primes p <= n} (1 + (n*(n+1)/2 - 1 - Sum_{i=2..n} s_p(i))/(p-1)), where s_p(i) is the sum of digits of i in base p. - _Amiram Eldar_, Jan 15 2025
%t A379742 DivisorSigma[0, FoldList[Times, Range[0, 30]!]] (* _Paolo Xausa_, Jan 06 2025 *)
%o A379742 (PARI) a(n)=numdiv(prod(k=1,n,k!));
%o A379742 vector(30,n,a(n-1)) \\ _Joerg Arndt_, Jan 02 2025
%o A379742 (PARI) a(n) = {my(prd = 1); forprime(p = 2, n, prd *= (1 + (n*(n+1)/2 - 1 - sum(i = 2, n, sumdigits(i, p)))/(p-1))); prd;} \\ _Amiram Eldar_, Jan 15 2025
%Y A379742 Cf. A000005, A000178, A027423.
%K A379742 nonn
%O A379742 0,3
%A A379742 _Tsuyoshi Hanatate_, Dec 31 2024