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A302054 a(n) is the sum of prime divisors of A302033(n).

%I A302054 #14 Apr 27 2018 17:11:30
%S A302054 0,2,5,3,8,10,7,5,12,14,17,15,10,12,9,7,18,20,23,21,26,28,25,23,16,18,
%T A302054 21,19,14,16,13,11,24,26,29,27,32,34,31,29,36,38,41,39,34,36,33,31,20,
%U A302054 22,25,23,28,30,27,25,18,20,23,21,16,18,15,13,30,32,35,33,38,40,37,35,42,44,47,45,40,42,39,37,48,50,53,51,56,58,55,53
%N A302054 a(n) is the sum of prime divisors of A302033(n).
%H A302054 Antti Karttunen, <a href="/A302054/b302054.txt">Table of n, a(n) for n = 0..8191</a>
%F A302054 a(n) = A001414(A302033(n)) = A008472(A302033(n)).
%t A302054 Array[Total@ Prime@ Flatten@ Position[#, 1] &@ Reverse@ IntegerDigits[BitXor[#, Floor[#/2]], 2] &, 88, 0] (* _Michael De Vlieger_, Apr 27 2018 *)
%o A302054 (PARI) first(n) = {my(pr = primes(1 + logint(n, 2)), ex = vector(#pr, i, 1), res = vector(n)); res[1] = 0; for(i = 1, n-1, v = valuation(i, 2); res[i + 1] = res[i] + pr[v++] * ex[v]; ex[v]*=-1); res}; \\ _David A. Corneth_, Apr 18 2018
%o A302054 (PARI)
%o A302054 A003188(n) = bitxor(n, n>>1);
%o A302054 A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
%o A302054 A302054(n) = vecsum(factor(A019565(A003188(n)))[, 1]); \\ _Antti Karttunen_, Apr 24 2018
%Y A302054 Cf. A001414, A008472, A302033.
%K A302054 nonn
%O A302054 0,2
%A A302054 _David A. Corneth_ & _Antti Karttunen_, Apr 18 2018