A252748 a(n) = A003961(n) - 2*n.

-1, -1, -1, 1, -3, 3, -3, 11, 7, 1, -9, 21, -9, 5, 5, 49, -15, 39, -15, 23, 13, -5, -17, 87, -1, -1, 71, 43, -27, 45, -25, 179, -1, -11, 7, 153, -33, -7, 7, 109, -39, 81, -39, 29, 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

Offset: 1

Author

Antti Karttunen, Dec 21 2014

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Partial sums: A252749.

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

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

Programs

Mathematica

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 *)

Scheme

(define (A252748 n) (- (A003961 n) (* 2 n)))

Formula

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

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

a(n) = A286385(n) - A033879(n). - Antti Karttunen, May 13 2017

Other identities. For all n >= 1:

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