A359427 - OEIS

%I #9 Jan 02 2023 16:48:55

%S 1,-2,-3,-2,-9,8,-5,6,-6,6,-45,-4,-25,-30,-21,-130,-225,-70,-125,-130,

%T -345,-570,-1125,-480,-544,-1150,-1812,-3550,-5625,222,-7,530,249,858,

%U 27,418,-35,430,45,610,-315,1520,-175,2650,-48,3450,-1575,2060,-850,804,-1275,-250,-7875,4288,-3565,6150,-12375

%N Dirichlet inverse of A358764.

%H Antti Karttunen, <a href="/A359427/b359427.txt">Table of n, a(n) for n = 1..11550</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F a(n) = A359428(n) - A358764(n).

%o (PARI)

%o up_to = 11550;

%o DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*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 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));

%o A060681(n) = (n-A032742(n));

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A358764(n) = A060681(A276086(n));

%o v359427 = DirInverseCorrect(vector(up_to,n,A358764(n)));

%o A359427(n) = v359427[n];

%Y Cf. A060681, A276086, A358764, A359428.

%Y Cf. A056911 (positions of odd terms), A323239 (parity of terms), A337945.

%Y Cf. also A342417.

%K sign,base

%O 1,2

%A _Antti Karttunen_, Jan 02 2023