A365714 - OEIS

%I #8 Sep 19 2023 15:32:36

%S 2,0,0,4,0,-4,0,8,1,-12,0,-4,0,12,6,16,0,-30,0,-12,-6,28,0,-8,9,20,15,

%T 12,0,-32,0,32,-14,-60,-18,-28,0,60,-10,-24,0,64,0,28,61,-52,0,-16,9,

%U 18,30,20,0,-66,-42,24,-30,-44,0,-20,0,44,-77,64,-30,-96,0,-60,26,160,0,-56,0,116,39,60,42,-96,0,-48,89

%N Sum of reversing binary value of n (A065620) and its Dirichlet inverse.

%H Antti Karttunen, <a href="/A365714/b365714.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n) = A065620(n) + A365713(n).

%F a(1) = 2, and for n > 1, a(n) = -Sum_{d|n, 1<d<n} A065620(d) * A365713(n/d).

%F a(4*n)/4 = A065620(n).

%o (PARI)

%o A065620(n, c=1) = sum(i=0, logint(n+!n, 2), if(bittest(n, i), (-1)^c++<<i)); \\ From A065620 by _M. F. Hasler_

%o memoA365713 = Map();

%o A365713(n) = if(1==n,1,my(v); if(mapisdefined(memoA365713,n,&v), v, v = -sumdiv(n,d,if(d<n,A065620(n/d)*A365713(d),0)); mapput(memoA365713,n,v); (v)));

%o A365714(n) = (A065620(n)+A365713(n));

%Y Cf. A065620, A365713.

%Y Cf. also A365712.

%K sign

%O 1,1

%A _Antti Karttunen_, Sep 19 2023