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.

A303915 a(n) = lambda(n)*E(n), where lambda(n) = A008836(n) and E(n) = A005361(n).

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%I A303915 #15 Apr 22 2025 04:57:48
%S A303915 1,-1,-1,2,-1,1,-1,-3,2,1,-1,-2,-1,1,1,4,-1,-2,-1,-2,1,1,-1,3,2,1,-3,
%T A303915 -2,-1,-1,-1,-5,1,1,1,4,-1,1,1,3,-1,-1,-1,-2,-2,1,-1,-4,2,-2,1,-2,-1,
%U A303915 3,1,3,1,1,-1,2,-1,1,-2,6,1,-1,-1,-2,1,-1,-1,-6,-1,1,-2,-2,1,-1,-1,-4,4,1,-1
%N A303915 a(n) = lambda(n)*E(n), where lambda(n) = A008836(n) and E(n) = A005361(n).
%H A303915 Vaclav Kotesovec, <a href="/A303915/b303915.txt">Table of n, a(n) for n = 1..10000</a>
%H A303915 Vaclav Kotesovec, <a href="/A303915/a303915.jpg">Graph - the asymptotic ratio (1000000 terms)</a>
%F A303915 Multiplicative with a(p^e) = e*(-1)^e, p prime and e > 0.
%F A303915 Dirichlet g.f.: (zeta(2*s))^2 / (zeta(s)*zeta(3*s)).
%F A303915 Dirichlet convolution with A048691(n) yields A092520(n).
%F A303915 Dirichlet inverse b(n), n>=1, is multiplicative with b(1)=1 and for p prime and e>0: b(p^e) = 0 if e mod 3 = 0 otherwise b(p^e) = (-1)^(3 - e mod 3).
%t A303915 Array[LiouvilleLambda[#] Apply[Times, FactorInteger[#][[All, -1]] ] &, 83] (* _Michael De Vlieger_, May 06 2018 *)
%o A303915 (PARI) a(n) = (-1)^bigomega(n)*factorback(factor(n)[, 2]); \\ _Michel Marcus_, May 05 2018
%Y A303915 Signed version of A005361.
%Y A303915 Cf. A008836, A048691, A092520.
%K A303915 sign,easy,mult
%O A303915 1,4
%A A303915 _Werner Schulte_, May 02 2018