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 A125073 #27 Sep 28 2023 04:24:45
%S A125073 0,1,1,0,1,2,1,3,0,2,1,1,1,2,2,0,1,1,1,1,2,2,1,4,0,2,3,1,1,3,1,0,2,2,
%T A125073 2,0,1,2,2,4,1,3,1,1,1,2,1,1,0,1,2,1,1,4,2,4,2,2,1,2,1,2,1,6,2,3,1,1,
%U A125073 2,3,1,3,1,2,1,1,2,3,1,1,0,2,1,2,2,2,2,4,1,2,2,1,2,2,2,1,1,1,1,0,1,3,1,4,3
%N A125073 a(n) = sum of the exponents in the prime factorization of n which are triangular numbers.
%H A125073 Antti Karttunen, <a href="/A125073/b125073.txt">Table of n, a(n) for n = 1..10000</a>
%H A125073 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.
%F A125073 Additive with a(p^e) = A010054(e)*e. - _Antti Karttunen_, Jul 08 2017
%F A125073 Sum_{k=1..n} a(k) ~ n * (log(log(n)) + B + C), where B is Mertens's constant (A077761) and C = -P(2) + Sum_{k>=2} (k*(k+1)/2) * (P(k*(k+1)/2) - P(k*(k+1)/2 + 1)) = -0.10099019472003733178..., where P(s) is the prime zeta function. - _Amiram Eldar_, Sep 28 2023
%e A125073 The prime factorization of 360 is 2^3 *3^2 *5^1. There are two exponents in this factorization which are triangular numbers, 1 and 3. So a(360) = 1 + 3 = 4.
%t A125073 f[n_] := Plus @@ Select[Last /@ FactorInteger[n], IntegerQ[Sqrt[8# + 1]] &];Table[f[n], {n, 110}] (* _Ray Chandler_, Nov 19 2006 *)
%o A125073 (PARI)
%o A125073 A010054(n) = issquare(8*n + 1); \\ This function from _Michael Somos_, Apr 27 2000.
%o A125073 A125073(n) = vecsum(apply(e -> (A010054(e)*e), factorint(n)[, 2])); \\ _Antti Karttunen_, Jul 08 2017
%Y A125073 Cf. A010054, A077761, A125072, A125030, A125071.
%K A125073 nonn,easy
%O A125073 1,6
%A A125073 _Leroy Quet_, Nov 18 2006
%E A125073 Extended by _Ray Chandler_, Nov 19 2006