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 A125071 #17 Sep 30 2023 21:56:06 %S A125071 0,1,1,0,1,2,1,0,0,2,1,1,1,2,2,4,1,1,1,1,2,2,1,1,0,2,0,1,1,3,1,0,2,2, %T A125071 2,0,1,2,2,1,1,3,1,1,1,2,1,5,0,1,2,1,1,1,2,1,2,2,1,2,1,2,1,6,2,3,1,1, %U A125071 2,3,1,0,1,2,1,1,2,3,1,5,4,2,1,2,2,2,2,1,1,2,2,1,2,2,2,1,1,1,1,0,1,3,1,1,3 %N A125071 a(n) = sum of the exponents in the prime factorization of n which are not primes. %H A125071 Antti Karttunen, <a href="/A125071/b125071.txt">Table of n, a(n) for n = 1..10000</a> %H A125071 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>. %F A125071 From _Amiram Eldar_, Sep 30 2023: (Start) %F A125071 Additive with a(p^e) = A191558(e). %F A125071 Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B - C), where B is Mertens's constant (A077761) and C = Sum_{p prime} p * (P(p) - P(p+1)) - Sum_{k>=2} P(k) = 0.20171354082810650948..., where P(s) is the prime zeta function. (End) %e A125071 720 has the prime-factorization of 2^4 *3^2 *5^1. Two of these exponents, 4 and 1, aren't primes. So a(720) = 4 + 1 = 5. %t A125071 f[n_] := Plus @@ Select[Last /@ FactorInteger[n], ! PrimeQ[ # ] &];Table[f[n], {n, 110}] (* _Ray Chandler_, Nov 19 2006 *) %o A125071 (PARI) A125071(n) = vecsum(apply(e -> if(isprime(e),0,e), factorint(n)[, 2])); \\ _Antti Karttunen_, Jul 07 2017 %Y A125071 Cf. A001222, A077761, A191558, A125070. %K A125071 nonn,easy %O A125071 1,6 %A A125071 _Leroy Quet_, Nov 18 2006 %E A125071 Extended by _Ray Chandler_, Nov 19 2006