cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A359427 Dirichlet inverse of A358764.

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%I A359427 #9 Jan 02 2023 16:48:55
%S A359427 1,-2,-3,-2,-9,8,-5,6,-6,6,-45,-4,-25,-30,-21,-130,-225,-70,-125,-130,
%T A359427 -345,-570,-1125,-480,-544,-1150,-1812,-3550,-5625,222,-7,530,249,858,
%U A359427 27,418,-35,430,45,610,-315,1520,-175,2650,-48,3450,-1575,2060,-850,804,-1275,-250,-7875,4288,-3565,6150,-12375
%N A359427 Dirichlet inverse of A358764.
%H A359427 Antti Karttunen, <a href="/A359427/b359427.txt">Table of n, a(n) for n = 1..11550</a>
%H A359427 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A359427 a(n) = A359428(n) - A358764(n).
%o A359427 (PARI)
%o A359427 up_to = 11550;
%o A359427 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 A359427 A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
%o A359427 A060681(n) = (n-A032742(n));
%o A359427 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A359427 A358764(n) = A060681(A276086(n));
%o A359427 v359427 = DirInverseCorrect(vector(up_to,n,A358764(n)));
%o A359427 A359427(n) = v359427[n];
%Y A359427 Cf. A060681, A276086, A358764, A359428.
%Y A359427 Cf. A056911 (positions of odd terms), A323239 (parity of terms), A337945.
%Y A359427 Cf. also A342417.
%K A359427 sign,base
%O A359427 1,2
%A A359427 _Antti Karttunen_, Jan 02 2023