%I #10 Sep 18 2017 09:26:04
%S 0,0,1,0,0,1,1,0,-1,0,2,1,1,1,2,0,0,-1,1,0,-1,2,2,1,-2,1,1,1,1,2,2,0,
%T 0,0,3,-1,1,1,3,0,0,-1,1,2,0,2,2,1,-3,-2,2,1,1,1,0,1,-1,1,2,2,1,2,1,0,
%U -1,0,2,0,0,3,3,-1,2,1,0,1,2,3,3,0,-1,0,4,-1,2,1,3,2,3,0,1,2,0,2,3,1,2,-3,2,-2,1,2,2,1,1
%N a(n) = 1 + A292377(n) - A292375(n).
%C Locate the node which contains n in binary tree A005940 and traverse towards the root (which is 1), counting separately all numbers of the form 4k+1 and of the form 4k+3 that occur on the path (including also starting n itself, if it is of the either form), until 1 is reached, which however, is never included in the count of 4k+1. a(n) is the count of 4k+3 numbers minus the count of 4k+1 numbers that were encountered.
%H Antti Karttunen, <a href="/A292378/b292378.txt">Table of n, a(n) for n = 1..16384</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = 1 + (A292377(n) - A292375(n)).
%F a(A000040(n)) = A038698(n).
%t a[1, 1] = 1; a[1, 3] = 0; a[n_, k_] := a[n, k] = a[Which[n == 1, 1, EvenQ@ n, n/2, True, Times @@ Power[Which[# == 1, 1, # == 2, 1, True, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger@ n], k] + Boole[Mod[n, 4] == k]; Array[a[#, 3] - a[#, 1] &, 105] (* _Michael De Vlieger_, Sep 17 2017 *)
%o (Scheme) (define (A292378 n) (+ 1 (- (A292377 n) (A292375 n))))
%Y Cf. A000040, A038698, A292375, A292377.
%K sign
%O 1,11
%A _Antti Karttunen_, Sep 17 2017