|
%I #12 Dec 21 2023 10:23:05
%S 0,1,1,2,2,2,5,4,5,8,7,8,0,1,9,14,7,6,13,16,17,20,5,20,6,16,21,4,25,
%T 24,29,10,15,28,25,32,35,1,9,34,-10,38,13,28,39,26,43,24,41,6,47,50,
%U 19,50,53,40,53,22,25,24,-4,52,-23,50,61,62,41,-8,63,68,61,24,23,19,65,74,21,42,73,64,39,76,13,80,48,40,81,-10,73,84,89,88,35,18,-5
%N a(n) = A285703(n) - n = A000203(A064216(n)) - n.
%H Antti Karttunen, <a href="/A285704/b285704.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A285703(n) - n = A000203(A064216(n)) - n.
%F Sum_{k=1..n} a(k) ~ c * n^2, where c = -1/2 + Product_{p prime} (p^3/((p+1)*(p^2-q(p)))) = 0.3168476756..., where q(p) = prevprime(p) (A151799) if p > 2 and q(2) = 1. - _Amiram Eldar_, Dec 21 2023
%t Table[-n + DivisorSigma[1, #] &@ If[n == 1, 1, Apply[Times, FactorInteger[2 n - 1] /. {p_, e_} /; p > 2 :> NextPrime[p, -1]^e]], {n, 95}] (* _Michael De Vlieger_, Apr 26 2017 *)
%o (Scheme) (define (A285704 n) (- (A285703 n) n))
%Y Cf. A000203, A001065, A064216, A151799, A285703, A285705.
%K sign
%O 1,4
%A _Antti Karttunen_, Apr 26 2017
|
