A323883 - OEIS

%I #5 Feb 08 2019 21:42:22

%S 1,-2,-3,0,-1,7,-1,2,2,2,-1,0,-1,2,3,-1,-1,-6,-1,0,3,2,-1,-11,0,2,3,0,

%T -1,-7,-1,-1,3,2,1,-1,-1,2,3,-2,-1,-7,-1,0,-2,2,-1,7,0,0,3,0,-1,-9,1,

%U -2,3,2,-1,0,-1,2,-2,3,1,-7,-1,0,3,-2,-1,20,-1,2,0,0,1,-7,-1,1,-6,2,-1,0,1,2,3,-2,-1,6,1,0,3,2,1,8

%N Dirichlet inverse of A322026.

%H Antti Karttunen, <a href="/A323883/b323883.txt">Table of n, a(n) for n = 1..20000</a>

%o (PARI)

%o up_to = 65537;

%o rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };

%o A007814(n) = valuation(n,2);

%o A007949(n) = valuation(n,3);

%o v322026 = rgs_transform(vector(up_to, n, [A007814(n), A007949(n)]));

%o DirInverse(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = -sumdiv(n, d, if(d<n, v[n/d]*u[d], 0))); (u) }; \\ Compute the Dirichlet inverse of the sequence given in input vector v.

%o v323883 = DirInverse(v322026);

%o A323883(n) = v323883[n];

%Y Cf. A007814, A007949, A322026, A323881, A323884.

%K sign

%O 1,2

%A _Antti Karttunen_, Feb 08 2019