cp's OEIS Frontend

A359165 Difference between A126760 and its Möbius transform.

%I A359165 #12 Dec 23 2022 11:25:41
%S A359165 0,1,1,1,1,1,1,1,1,2,1,1,1,3,2,1,1,1,1,2,3,4,1,1,2,5,1,3,1,2,1,1,4,6,
%T A359165 4,1,1,7,5,2,1,3,1,4,2,8,1,1,3,9,6,5,1,1,5,3,7,10,1,2,1,11,3,1,6,4,1,
%U A359165 6,8,12,1,1,1,13,9,7,6,5,1,2,1,14,1,3,7,15,10,4,1,2,7,8,11,16,8,1,1,17
%N A359165 Difference between A126760 and its Möbius transform.
%H A359165 Antti Karttunen, <a href="/A359165/b359165.txt">Table of n, a(n) for n = 1..12000</a>
%H A359165 Antti Karttunen, <a href="/A359165/a359165.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A359165 a(n) = A126760(n) - A347233(n).
%F A359165 a(n) = Sum_{d|n, d<n} A347233(d).
%F A359165 a(n) = -Sum_{d|n, d<n} A008683(n/d)*A126760(d).
%o A359165 (PARI)
%o A359165 A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760.
%o A359165 A347233(n) = sumdiv(n,d,moebius(n/d)*A126760(d));
%o A359165 A359165(n) = (A126760(n)-A347233(n));
%Y A359165 Cf. A008683, A126760, A347233.
%Y A359165 Cf. also A323882, A359164.
%K A359165 nonn
%O A359165 1,10
%A A359165 _Antti Karttunen_, Dec 22 2022