A353460 - OEIS

%I #10 Apr 20 2022 22:48:39

%S 1,0,-1,0,-1,0,-1,0,-2,0,-2,0,-2,0,-1,0,-3,0,-3,0,-2,0,-4,0,-1,0,-4,0,

%T -5,0,-5,0,-3,0,1,0,-6,0,-4,0,-7,0,-7,0,0,0,-8,0,-4,0,-5,0,-9,0,3,0,

%U -6,0,-10,0,-10,0,-1,0,2,0,-11,0,-7,0,-12,0,-12,0,-3,0,1,0,-13,0,-8,0,-14,0,4,0,-9,0,-15,0,0,0

%N Dirichlet convolution of A126760 with A349134 (the Dirichlet inverse of Kimberling's paraphrases).

%C Taking the Dirichlet convolution between this sequence and A349371 gives A349393, and similarly for many other such analogous pairs.

%H Antti Karttunen, <a href="/A353460/b353460.txt">Table of n, a(n) for n = 1..65537</a>

%F a(n) = Sum_{d|n} A126760(d) * A349134(n/d).

%o (PARI)

%o A003602(n) = (1+(n>>valuation(n,2)))/2;

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

%o memoA349134 = Map();

%o A349134(n) = if(1==n,1,my(v); if(mapisdefined(memoA349134,n,&v), v, v = -sumdiv(n,d,if(d<n,A003602(n/d)*A349134(d),0)); mapput(memoA349134,n,v); (v)));

%o A353460(n) = sumdiv(n,d,A126760(d)*A349134(n/d));

%Y Cf. A003602, A126760, A349134, A353461 (Dirichlet inverse), A353462 (sum with it).

%Y Cf. also A349371, A349380, A349393, A349432.

%K sign

%O 1,9

%A _Antti Karttunen_, Apr 20 2022