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

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, 21, 19, 14, 16, 13, 11, 24, 26, 29, 27, 32, 34, 31, 29, 36, 38, 41, 39, 34, 36, 33, 31, 20, 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

Offset: 0

Author

David A. Corneth & Antti Karttunen, Apr 18 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191

Crossrefs

Cf. A001414, A008472, A302033.

Programs

Mathematica

Array[Total@ Prime@ Flatten@ Position[#, 1] &@ Reverse@ IntegerDigits[BitXor[#, Floor[#/2]], 2] &, 88, 0] (* Michael De Vlieger, Apr 27 2018 *)

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

PARI

A003188(n) = bitxor(n, n>>1);
A019565(n) = {my(j,v); factorback(Mat(vector(if(n, #n=vecextract(binary(n), "-1..1")), j, [prime(j), n[j]])~))}; \\ From A019565
A302054(n) = vecsum(factor(A019565(A003188(n)))[, 1]); \\ Antti Karttunen, Apr 24 2018

Formula

a(n) = A001414(A302033(n)) = A008472(A302033(n)).