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.

A236441 Möbius inversion of A235342.

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%I A236441 #21 Aug 29 2017 03:38:29
%S A236441 0,1,0,1,-2,0,-1,1,0,0,-2,0,-2,0,0,1,-2,0,-1,0,0,0,2,0,-2,0,0,0,1,0,1,
%T A236441 1,0,0,0,0,-1,0,0,0,1,0,0,0,0,0,-1,0,-1,0,0,0,3,0,0,0,0,0,0,0,0,0,0,1,
%U A236441 0,0,-2,0,0,0,0,0,-3,0,0,0,0,0,7,0,0,0,-4,0,0,0,0,0,0,0,0,0,0,0,0,0,-3,0,0,0,5,0,1,0,0,0,-2,0,-2,0,0,0,1,0,0,0,0,0,0,0,-2
%N A236441 Möbius inversion of A235342.
%C A236441 Möbius inversion of A235342. Since b(xy) = b(x)+b(y) where b = A235342, it follows that a(n) is zero on nonprime powers and b(p) if n=p^k.
%H A236441 Antti Karttunen, <a href="/A236441/b236441.txt">Table of n, a(n) for n = 1..5041</a>
%H A236441 Alexander Riasanovsky, <a href="/A236441/a236441.txt">Sage program</a>
%F A236441 For n > 0, a(n) = Sum_{d|n} b(d)*mu(n/d) where b(n) = A235342(n).
%e A236441 a(1)=0 since 1 is not a prime power.
%e A236441 a(2)=b(2)=1 since 2=2! and b(2!)=1.
%e A236441 a(3)=b(3)=0 since 3=3!/2! and b(3!/2!)=b(3!)-b(2!)=1-1=0.
%e A236441 a(4)=b(2)=1 (above).
%e A236441 a(5)=b(5)=-2 since 5=5!/(3!2!2!) and b(5!/(3!2!2!))=1-3=-2.
%e A236441 a(6)=0 since 6 is not a prime power.
%Y A236441 Möbius inversion of A235342.
%K A236441 sign
%O A236441 1,5
%A A236441 _Alexander Riasanovsky_, Jan 25 2014
%E A236441 Data section extended and b-file computed with Riasanovsky's Sage program by _Antti Karttunen_, Mar 28 2017