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A285703 a(n) = A000203(A064216(n)). 6

%I #12 Dec 21 2023 10:23:19

%S 1,3,4,6,7,8,12,12,14,18,18,20,13,15,24,30,24,24,32,36,38,42,28,44,31,

%T 42,48,32,54,54,60,42,48,62,60,68,72,39,48,74,31,80,56,72,84,72,90,72,

%U 90,56,98,102,72,104,108,96,110,80,84,84,57,114,40,114,126,128,108,60,132,138,132,96,96,93,140,150,98,120,152,144,120,158,96,164,133,126

%N a(n) = A000203(A064216(n)).

%H Antti Karttunen, <a href="/A285703/b285703.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A000203(A064216(n)).

%F Sum_{k=1..n} a(k) ~ c * n^2, where c = Product_{p prime} (p^3/((p+1)*(p^2-q(p)))) = 0.8168476756..., where q(p) = prevprime(p) (A151799) if p > 2 and q(2) = 1. - _Amiram Eldar_, Dec 21 2023

%t Table[DivisorSigma[1, #] &@ If[n == 1, 1, Apply[Times, FactorInteger[2 n - 1] /. {p_, e_} /; p > 2 :> NextPrime[p, -1]^e]], {n, 86}] (* _Michael De Vlieger_, Apr 26 2017 *)

%o (Scheme) (define (A285703 n) (A000203 (A064216 n)))

%Y Cf. A000203, A064216, A099774, A151799, A285702, A285704, A285705.

%K nonn

%O 1,2

%A _Antti Karttunen_, Apr 26 2017

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