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A333352 a(n) is the product of indices of the smallest and greatest prime factors of n.

%I A333352 #13 Mar 16 2020 18:17:27
%S A333352 1,1,4,1,9,2,16,1,4,3,25,2,36,4,6,1,49,2,64,3,8,5,81,2,9,6,4,4,100,3,
%T A333352 121,1,10,7,12,2,144,8,12,3,169,4,196,5,6,9,225,2,16,3,14,6,256,2,15,
%U A333352 4,16,10,289,3,324,11,8,1,18,5,361,7,18,4,400,2,441,12,6,8,20,6,484,3
%N A333352 a(n) is the product of indices of the smallest and greatest prime factors of n.
%H A333352 Peter Kagey, <a href="/A333352/b333352.txt">Table of n, a(n) for n = 1..10000</a>
%H A333352 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A333352 If n = Product (p_j^k_j) then a(n) = min{pi(p_j)} * max{pi(p_j)}, where pi = A000720.
%F A333352 a(n) = A055396(n) * A061395(n) for n > 1.
%F A333352 a(2*n) = A061395(n) for n > 1.
%F A333352 a(n^k) = a(n) for k > 0
%F A333352 a(2*prime(n)^k) = n for k > 0.
%F A333352 a(prime(n)^k) = n^2 for k > 0.
%F A333352 a(n!) = pi(n) for n > 1.
%F A333352 a(A002110(n)) = n.
%e A333352 a(315) = a(3^2 * 5 * 7) = a(prime(2)^2 * prime(3) * prime(4)) = 2 * 4 = 8.
%t A333352 a[1] = 1; a[n_] := PrimePi[FactorInteger[n] [[1, 1]]] PrimePi[ FactorInteger[ n] [[-1, 1]]]; Table[a[n], {n, 1, 80}]
%o A333352 (PARI) a(n) = if (n==1, 1, my(f=factor(n)[,1]); primepi(vecmin(f))*primepi(vecmax(f))); \\ _Michel Marcus_, Mar 16 2020
%Y A333352 Cf. A000079 (positions of 1's), A000720, A002110, A006530, A020639, A033845 (positions of 2's), A055396, A061395, A066048, A156061, A243055.
%K A333352 nonn
%O A333352 1,3
%A A333352 _Ilya Gutkovskiy_, Mar 15 2020