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a(n) = A003961(n) - 2*n.
27

%I #23 May 14 2017 00:12:01

%S -1,-1,-1,1,-3,3,-3,11,7,1,-9,21,-9,5,5,49,-15,39,-15,23,13,-5,-17,87,

%T -1,-1,71,43,-27,45,-25,179,-1,-11,7,153,-33,-7,7,109,-39,81,-39,29,

%U 85,-5,-41,309,23,47,-7,49,-47,267,-19,185,1,-23,-57,195,-55,-13,149,601,-11,63,-63,35,7,91,-69,531,-67,-25,95,55,-11,99

%N a(n) = A003961(n) - 2*n.

%H Antti Karttunen, <a href="/A252748/b252748.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A003961(n) - 2*n.

%F a(n) = A252750(A156552(n)).

%F a(n) = A286385(n) - A033879(n). - _Antti Karttunen_, May 13 2017

%F Other identities. For all n >= 1:

%F sign(a(n)) = (-1)^(1+A252742(n)).

%t Table[Times @@ Map[#1^#2 & @@ # &, FactorInteger[n] /. {p_, e_} /; e > 0 :> {Prime[PrimePi@ p + 1], e}] - Boole[n == 1] - 2 n, {n, 78}] (* _Michael De Vlieger_, May 14 2017 *)

%o (Scheme) (define (A252748 n) (- (A003961 n) (* 2 n)))

%Y Partial sums: A252749.

%Y Cf. A246282 (positions of the positive terms), A252742 (their characteristic function).

%Y Cf. A003961, A033879, A252750, A156552, A249820, A286385, A286448.

%K sign

%O 1,5

%A _Antti Karttunen_, Dec 21 2014