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 A378181 #5 Nov 24 2024 09:38:54
%S A378181 0,1,1,2,1,3,1,3,2,3,1,6,1,3,3,4,1,6,1,6,3,3,1,10,2,3,3,6,1,10,1,5,3,
%T A378181 3,3,10,1,3,3,10,1,10,1,6,6,3,1,15,2,6,3,6,1,10,3,10,3,3,1,20,1,3,6,6,
%U A378181 3,10,1,6,3,10,1,15,1,3,6,6,3,10,1,15,4,3,1
%N A378181 a(1) = 0, a(n) = binomial(bigomega(n) + omega(n) - 1, omega(n)), where bigomega = A001222 and omega = A001221.
%H A378181 Michael De Vlieger, <a href="/A378181/b378181.txt">Table of n, a(n) for n = 1..10000</a>
%F A378181 a(n) = cardinality of { m : rad(m) | n, bigomega(m) < bigomega(n) }, i.e., row n of A378180.
%F A378181 For prime p, a(p) = A010846(p)-1 = A000005(p)-1 = 1.
%F A378181 For prime power p^k, a(p^k) = A010846(p^k)-1 = A000005(p^k)-1 = k.
%F A378181 For n in A024619, a(n) != A010846(n).
%t A378181 {0}~Join~Table[Binomial[PrimeOmega[n] + # - 1, #] &@ PrimeNu[n], {n, 120}]
%Y A378181 Cf. A000005, A001221, A001222, A007947, A010846, A024619, A378180.
%K A378181 nonn,easy
%O A378181 1,4
%A A378181 _Michael De Vlieger_, Nov 19 2024