%I
%S 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 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 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 a(n) = sum of the exponents in the primefactorization of n which are triangular numbers.
%H Antti Karttunen, <a href="/A125073/b125073.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F Additive with a(p^e) = A010054(e)*e.  _Antti Karttunen_, Jul 08 2017
%e The primefactorization 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 f[n_] := Plus @@ Select[Last /@ FactorInteger[n], IntegerQ[Sqrt[8# + 1]] &];Table[f[n], {n, 110}] (* _Ray Chandler_, Nov 19 2006 *)
%o (PARI)
%o A010054(n) = issquare(8*n + 1); \\ This function from _Michael Somos_, Apr 27 2000.
%o A125073(n) = vecsum(apply(e > (A010054(e)*e), factorint(n)[, 2])); \\ _Antti Karttunen_, Jul 08 2017
%Y Cf. A010054, A125072, A125030, A125071.
%K nonn
%O 1,6
%A _Leroy Quet_, Nov 18 2006
%E Extended by _Ray Chandler_, Nov 19 2006
