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

0,2

Links

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A001414, A008472, A302033.

Sequence in context: A136189 A309557 A292965 * A081146 A261927 A262870

Adjacent sequences: A302051 A302052 A302053 * A302055 A302056 A302057

Keyword

nonn

Author

David A. Corneth & Antti Karttunen, Apr 18 2018

Status

approved