A252749 -id:A252749 - cp's OEIS frontend

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

Antti Karttunen, Dec 21 2014

sign

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

Partial sums: A252749.
Cf. A246282 (positions of the positive terms), A252742 (their characteristic function).
Cf. A003961, A033879, A252750, A156552, A249820, A286385, A286448.

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 *)

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

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)).

A252751 Partial sums of A252750: a(0) = 0; for >= 1: a(n) = A252750(n) + a(n-1).

Original entry on oeis.org

0, -1, -2, -1, -4, -1, 6, 17, 14, 15, 20, 41, 40, 79, 150, 199, 190, 195, 208, 231, 238, 283, 368, 455, 478, 525, 620, 773, 866, 1133, 1596, 1775, 1766, 1761, 1760, 1803, 1784, 1865, 2014, 2123, 2112, 2203, 2378, 2573, 2762, 3107, 3712, 4021, 3948, 4115, 4426, 4667, 5024, 5459, 6234, 6765, 7410, 7939, 8904, 9813, 10964, 12515, 15154, 15755, 15740

Offset: 0

Antti Karttunen, Dec 21 2014

sign

Antti Karttunen, Table of n, a(n) for n = 0..8191

Cf. A252750, A252749.

a(0) = 0; for >= 1: a(n) = A252750(n) + a(n-1).

cp's OEIS Frontend

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

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