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 A056672 #18 Jun 03 2023 23:56:33
%S A056672 1,2,4,2,4,2,4,4,4,2,4,4,8,4,4,4,8,8,16,16,16,8,16,16,16,8,8,8,16,16,
%T A056672 32,32,32,16,16,16,32,16,16,16,32,32,64,64,64,32,64,64,64,64,64,64,
%U A056672 128,128,128,128,128,64,128,128,256,128,128,128,128,128,256,256,256,256
%N A056672 Number of unitary and squarefree divisors of n! Also, number of divisors of the special squarefree part of n!, A055773(n).
%C A056672 The divisor d=1 is counted here as being free of prime divisors and also unitary.
%H A056672 Amiram Eldar, <a href="/A056672/b056672.txt">Table of n, a(n) for n = 1..10000</a>
%F A056672 a(n) = A000005(A055231(n!)).
%F A056672 a(n) = A000005(A007913(n!)/A055229(n!)).
%F A056672 a(n) = A000005(A055773(n)).
%F A056672 a(n) = 2^A056171(n). - _Kevin Ryde_, Jun 03 2023
%e A056672 n=11: 11! = 2*2*2*2*2*2*2*2*3*3*3*3*5*5*7*11, has 540 divisors, 32 are unitary and 32 are squarefree. Only 4 divisors, {1,7,11,77} have both properties, so a(11)=4.
%t A056672 rad[n_] := Times @@ First /@ FactorInteger[n]; p[n_] := Denominator[n/rad[n]^2]; a[n_] := DivisorSigma[0, p[n!]]; Array[a, 70] (* _Amiram Eldar_, Sep 22 2019 *)
%o A056672 (PARI) a(n) = my(f=n!); sumdiv(f, d, issquarefree(d) && (gcd(d, f/d) == 1)); \\ _Michel Marcus_, Sep 05 2017
%o A056672 (PARI) a(n) = 1 << (primepi(n) - primepi(n>>1)); \\ _Kevin Ryde_, Jun 03 2023
%Y A056672 Cf. A000005, A000142, A007913, A055229, A055231, A055773, A056171.
%K A056672 nonn,easy
%O A056672 1,2
%A A056672 _Labos Elemer_, Aug 10 2000