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 A056172 #26 Jul 24 2024 21:09:30
%S A056172 0,0,0,1,1,2,2,2,2,3,3,3,3,4,4,4,4,4,4,4,4,5,5,5,5,6,6,6,6,6,6,6,6,7,
%T A056172 7,7,7,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,11,11,11,
%U A056172 11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,13,13,13,13,14,14,14
%N A056172 Number of non-unitary prime divisors of n!.
%C A056172 A non-unitary prime divisor for n! cannot exceed n/2.
%H A056172 G. C. Greubel, <a href="/A056172/b056172.txt">Table of n, a(n) for n = 1..1000</a>
%F A056172 a(n) = pi(n/2).
%F A056172 A prime divisor of x is non-unitary iff its exponent is at least 2 in the prime power factorization of x. In general, GCD(p, x/p) = 1 or p. Cases are counted when GCD(p, n/p) > 1.
%F A056172 a(n) = A000720(n) - A056171(n). - _Robert G. Wilson v_, Apr 09 2017
%F A056172 a(n) = A056170(n!). - _Amiram Eldar_, Jul 24 2024
%e A056172 10! = 2^8 * 3^4 * 5^2 * 7. The non-unitary prime divisors are 2, 3, and 5 because their exponents exceed 1, so a(10) = 3. The only unitary prime divisor of 10! is 7.
%p A056172 with(numtheory); A056172:=n->pi(floor(n/2)); seq(A056172(k),k=1..100); # _Wesley Ivan Hurt_, Sep 30 2013
%t A056172 Table[PrimePi[Floor[n/2]], {n,100}] (* _Wesley Ivan Hurt_, Sep 30 2013 *)
%Y A056172 Cf. A000720, A001221, A034444, A048105, A048656, A048657, A056170, A056171.
%K A056172 nonn,easy
%O A056172 1,6
%A A056172 _Labos Elemer_, Jul 27 2000
%E A056172 Example corrected by _Jon E. Schoenfield_, Sep 30 2013