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.

A319993 a(n) = A319997(n) / A173557(n).

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%I A319993 #10 Nov 08 2018 21:13:17
%S A319993 1,-1,1,0,1,-1,1,0,3,-1,1,0,1,-1,1,0,1,-3,1,0,1,-1,1,0,5,-1,9,0,1,-1,
%T A319993 1,0,1,-1,1,0,1,-1,1,0,1,-1,1,0,3,-1,1,0,7,-5,1,0,1,-9,1,0,1,-1,1,0,1,
%U A319993 -1,3,0,1,-1,1,0,1,-1,1,0,1,-1,5,0,1,-1,1,0,27,-1,1,0,1,-1,1,0,1,-3,1,0,1,-1,1,0,1,-7,3,0,1,-1,1,0,1
%N A319993 a(n) = A319997(n) / A173557(n).
%H A319993 Antti Karttunen, <a href="/A319993/b319993.txt">Table of n, a(n) for n = 1..20000</a>
%F A319993 Multiplicative with a(2^1) = -1, a(2^e) = 0 for e > 1, and a(p^e) = p^(e-1) when p is an odd prime.
%F A319993 a(n) = A319997(n) / A173557(n).
%F A319993 a(2n) = A003557(2n) - 2*A003557(n), a(2n+1) = A003557(2n+1).
%o A319993 (PARI) A319993(n) =  { my(f=factor(n)); prod(i=1,#f~,if(2==f[i,1],-(1==f[i,2]),(f[i,1]^(f[i,2]-1)))); };
%o A319993 (PARI)
%o A319993 A173557(n) = factorback(apply(p -> p-1, factor(n)[, 1]));
%o A319993 A319997(n) = sumdiv(n,d,(d%2)*moebius(n/d)*d);
%o A319993 A319993(n) = (A319997(n)/A173557(n));
%Y A319993 Cf. A003557, A173557, A319997, A319999.
%K A319993 sign,mult
%O A319993 1,9
%A A319993 _Antti Karttunen_, Nov 08 2018