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 A080256 #18 Sep 28 2023 04:23:06
%S A080256 0,2,2,3,2,4,2,4,3,4,2,5,2,4,4,5,2,5,2,5,4,4,2,6,3,4,4,5,2,6,2,6,4,4,
%T A080256 4,6,2,4,4,6,2,6,2,5,5,4,2,7,3,5,4,5,2,6,4,6,4,4,2,7,2,4,5,7,4,6,2,5,
%U A080256 4,6,2,7,2,4,5,5,4,6,2,7,5,4,2,7,4,4,4,6,2,7,4,5,4,4,4,8,2,5,5,6,2,6,2,6,6
%N A080256 Sum of numbers of distinct and of all prime factors of n.
%C A080256 a(n) = 2 iff n is prime, A000040; a(n) > 2 iff n is composite, A002808; a(n) <= 3 iff n is prime or square of prime, A000430; a(n) = 3 iff n is square of prime, A001248; a(A080257(n)) > 3;
%C A080256 a(n) <= 4 iff product of proper divisors <= n^2, A007964; a(n) = 4 iff n has four divisors, A030513; a(n) > 4 iff product of proper divisors > n^2, A058080; a(A064598(n)) <= 5; a(A080258(n)) = 5.
%H A080256 G. C. Greubel, <a href="/A080256/b080256.txt">Table of n, a(n) for n = 1..5000</a>
%F A080256 a(n) = Omega(n) + omega(n) = A001221(n) + A001222(n).
%F A080256 Additive with a(p^e) = e + 1.
%F A080256 Sum_{k=1..n} a(k) = 2 * n * log(log(n)) + c * n + O(n/log(n)), where c = A077761 + A083342 = 1.29615109474508069537... . - _Amiram Eldar_, Sep 28 2023
%t A080256 f[n_] := Plus @@ (Last /@ FactorInteger[n] + 1); Table[ f[n], {n, 105}] (* _Robert G. Wilson v_, Aug 03 2005 *)
%o A080256 (PARI) a(n) = {my(f = factor(n)); omega(f) + bigomega(f);} \\ _Amiram Eldar_, Sep 28 2023
%Y A080256 Cf. A000040, A000430, A002808, A001248, A007964, A058080, A064598, A080257, A080258.
%Y A080256 Cf. A001221, A001222, A046660, A077761, A083342.
%K A080256 nonn,easy
%O A080256 1,2
%A A080256 _Reinhard Zumkeller_, Feb 10 2003