A364288 - OEIS

%I #13 Jul 25 2023 13:11:23

%S 1,1,0,2,-2,0,-8,4,4,-4,-20,0,-50,-16,2,8,-110,8,-236,-8,-8,-40,-488,

%T 0,14,-100,18,-32,-994,4,-2016,16,-28,-220,8,16,-4058,-472,-86,-16,

%U -8150,-16,-16340,-80,20,-976,-32720,0,26,28,-202,-200,-65482,36,-4,-64,-452,-1988,-131012,8,-262082,-4032,6,32,-58,-56

%N a(n) = n - A243071(n).

%H Antti Karttunen, <a href="/A364288/b364288.txt">Table of n, a(n) for n = 1..12288</a>

%F a(n) = A364258(A243071(n)).

%F For n >= 1, a(2*n) = 2*a(n).

%F For n >= 0, a(A007283(n)) = 0.

%t nn = 60; f[x_] := Times @@ Power[Which[# == 1, 1, # == 2, 1, True, NextPrime[#, -1]] & /@ First[#], Last[#] ] &@ Transpose@ FactorInteger@ x; Do[a[n] = Which[n <= 2, n - 1, OddQ[n], 1 + 2 a[f[n]], True, 2 a[n/2] ], {n, nn}]; Array[# - a[#] &, nn] (* _Michael De Vlieger_, Jul 25 2023 *)

%o (PARI)

%o A064989(n) = { my(f=factor(n>>valuation(n,2))); for(i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f); };

%o A243071(n) = if(n<=2, n-1, if(!(n%2), 2*A243071(n/2), 1+(2*A243071(A064989(n)))));

%o A364288(n) = (n-A243071(n));

%Y Cf. A243071, A364256 [= gcd(n,a(n))], A364258.

%Y Cf. A007283 (positions of 0's, conjectured), A364289 (positions of terms <= 0), A364290 (of terms > 0), A364291 (of terms >= 0).

%Y Cf. also A364253.

%K sign

%O 1,4

%A _Antti Karttunen_, Jul 25 2023