cp's OEIS Frontend

A340189 a(n) = n + A340187(n).

%I A340189 #7 Dec 31 2020 15:34:59
%S A340189 2,1,1,4,1,9,1,8,11,17,1,11,1,25,27,16,1,13,1,17,41,41,1,24,37,49,25,
%T A340189 21,1,1,1,32,69,65,79,40,1,73,83,40,1,-7,1,35,21,89,1,48,79,17,111,39,
%U A340189 1,61,131,60,125,113,1,83,1,121,27,64,145,-27,1,53,153,-49,1,71,1,145,23,57,193,-31,1,80,83,161,1,131
%N A340189 a(n) = n + A340187(n).
%H A340189 Antti Karttunen, <a href="/A340189/b340189.txt">Table of n, a(n) for n = 1..8191</a>
%H A340189 Antti Karttunen, <a href="/A340189/a340189.txt">Data supplement: n, a(n) computed for n = 1..65537</a>
%F A340189 a(n) = n + A340187(n).
%F A340189 a(n) = A340188(n) + A318828(n).
%o A340189 (PARI)
%o A340189 up_to = 65537;
%o A340189 A063994(n) = { my(f=factor(n)); prod(i=1, #f~, gcd(f[i, 1]-1, n-1)); };
%o A340189 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 A340189 v340187 = DirInverse(vector(up_to, n, A063994(n)));
%o A340189 A340187(n) = v340187[n];
%o A340189 A340189(n) = (n+A340187(n));
%Y A340189 Cf. A063994, A318828, A340187, A340188.
%Y A340189 Cf. also A318833.
%K A340189 sign
%O A340189 1,1
%A A340189 _Antti Karttunen_, Dec 31 2020