A294898 a(n) = A005187(n) - A000203(n).

0, 0, 0, 0, 2, -2, 3, 0, 3, 0, 7, -6, 9, 1, 2, 0, 14, -5, 15, -4, 7, 5, 18, -14, 16, 7, 10, -3, 24, -16, 25, 0, 16, 12, 19, -21, 33, 13, 18, -12, 37, -15, 38, 1, 8, 16, 41, -30, 38, 4, 26, 3, 48, -16, 33, -11, 30, 22, 53, -52, 55, 23, 16, 0, 44, -14, 63, 8, 39, -7, 66, -53, 69, 31, 22, 9, 54, -16, 73, -28, 38, 35, 78, -59, 58

Offset

1,5

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Index entries for sequences related to sigma(n).

Formula

a(n) = A005187(n) - A000203(n).

a(n) = A011371(n) - A001065(n).

a(n) = A033879(n) - A000120(n).

Sum_{k=1..n} a(k) ~ c * n^2, where c = 1 - zeta(2)/2 = 0.177532... . - Amiram Eldar, Feb 22 2024

Mathematica

Array[IntegerExponent[(2 #)!, 2] - DivisorSigma[1, #] &, 85] (* Michael De Vlieger, Nov 26 2017 *)

Prog

(Scheme) (define (A294898 n) (- (A005187 n) (A000203 n)))

Crossrefs

Cf. A000120, A000203, A001065, A005187, A011371, A013661, A033879, A294896, A294899.

Cf. A295296 (positions of zeros), A295297 (parity of a(n)).

Sequence in context: A138067 A324348 A125093 * A297114 A318448 A103516

Adjacent sequences: A294895 A294896 A294897 * A294899 A294900 A294901

Keyword

sign

Author

Antti Karttunen, Nov 25 2017

Status

approved