A304527 - OEIS

%I #13 Dec 04 2022 13:06:04

%S 0,1,1,2,1,6,1,3,5,11,1,5,1,15,14,8,1,5,1,10,18,21,1,12,10,29,6,14,1,

%T 8,1,17,24,34,23,15,1,38,32,23,1,12,1,20,12,44,1,25,14,23,37,28,1,28,

%U 29,31,41,58,1,34,1,62,16,31,37,18,1,33,47,22,1,39,1,68,25,37,33,26,1,49,22,75,1,50,42,82,61,46,1,58,41,43,65,90,46,59,1

%N Difference between A064664 (the inverse of EKG-sequence) and its Möbius-transform.

%H Antti Karttunen, <a href="/A304527/b304527.txt">Table of n, a(n) for n = 1..32768</a>

%H <a href="/index/Ed#EKG">Index entries for sequences related to EKG sequence</a>

%F a(n) = A064664(n) - A304526(n).

%F a(n) = Sum_{d|n, d<n} A304526(d).

%F a(n) = -Sum_{d|n, d<n} A008683(n/d)*A064664(d).

%F For n >= 2, a(2*A000040(n))-1 = a(4*A000040(n)) = A064955(n). - _Antti Karttunen_, Dec 04 2022

%o (PARI) A304527(n) = -sumdiv(n, d, (d<n)*moebius(n/d)*A064664(d));

%Y Cf. A000040, A008683, A064664, A064955, A304526.

%K nonn

%O 1,4

%A _Antti Karttunen_, May 18 2018