A359165 - OEIS

%I #12 Dec 23 2022 11:25:41

%S 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 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 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 Difference between A126760 and its Möbius transform.

%H Antti Karttunen, <a href="/A359165/b359165.txt">Table of n, a(n) for n = 1..12000</a>

%H Antti Karttunen, <a href="/A359165/a359165.txt">Data supplement: n, a(n) computed for n = 1..100000</a>

%F a(n) = A126760(n) - A347233(n).

%F a(n) = Sum_{d|n, d<n} A347233(d).

%F a(n) = -Sum_{d|n, d<n} A008683(n/d)*A126760(d).

%o (PARI)

%o A126760(n) = {n&&n\=3^valuation(n, 3)<<valuation(n, 2); n%3+n\6*2}; \\ From A126760.

%o A347233(n) = sumdiv(n,d,moebius(n/d)*A126760(d));

%o A359165(n) = (A126760(n)-A347233(n));

%Y Cf. A008683, A126760, A347233.

%Y Cf. also A323882, A359164.

%K nonn

%O 1,10

%A _Antti Karttunen_, Dec 22 2022