A349369 - OEIS

%I #8 Nov 25 2021 19:39:29

%S 2,0,0,9,0,12,0,3,4,42,0,-10,0,54,28,37,0,16,0,-41,36,90,0,60,49,102,

%T 16,-39,0,-84,0,11,60,138,126,30,0,150,68,221,0,-92,0,-81,40,186,0,

%U -72,81,-61,92,-79,0,36,210,259,100,234,0,394,0,246,56,149,238,-172,0,-121,124,-352,0,8,0,294,-22,-119,270

%N Sum of A006369 and its Dirichlet inverse, where A006369 is the inverse of "amusical permutation", A006368.

%H Antti Karttunen, <a href="/A349369/b349369.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = A006369(n) + A349368(n).

%F a(1) = 2, and for n >1, a(n) = -Sum_{d|n, 1<d<n} A006369(d) * A349368(n/d).

%o (PARI)

%o A006369(n) = if(!(n%3),(2/3)*n,(1/3)*if(1==(n%3),((4*n)-1),((4*n)+1)));

%o memoA349368 = Map();

%o A349368(n) = if(1==n,1,my(v); if(mapisdefined(memoA349368,n,&v), v, v = -sumdiv(n,d,if(d<n,A006369(n/d)*A349368(d),0)); mapput(memoA349368,n,v); (v)));

%o A349369(n) = (A006369(n)+A349368(n));

%Y Cf. A006369, A349368.

%Y Cf. also A349352, A349378.

%K sign

%O 1,1

%A _Antti Karttunen_, Nov 17 2021