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a(n) = A005187(n) - A000203(n).
27

%I #21 Feb 22 2024 02:12:07

%S 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,

%T 24,-16,25,0,16,12,19,-21,33,13,18,-12,37,-15,38,1,8,16,41,-30,38,4,

%U 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

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

%H Antti Karttunen, <a href="/A294898/b294898.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

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

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

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

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

%t Array[IntegerExponent[(2 #)!, 2] - DivisorSigma[1, #] &, 85] (* _Michael De Vlieger_, Nov 26 2017 *)

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

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

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

%K sign

%O 1,5

%A _Antti Karttunen_, Nov 25 2017