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.

A068101 a(n) = Sum_{k|n, k<=sqrt(n)} mu(k) where mu(k) is the Moebius function and the sum is over the positive divisors k of n with k <= sqrt(n).

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%I A068101 #27 Oct 09 2017 02:17:52
%S A068101 1,1,1,0,1,0,1,0,0,0,1,-1,1,0,0,0,1,-1,1,0,0,0,1,-1,0,0,0,0,1,-2,1,0,
%T A068101 0,0,0,0,1,0,0,-1,1,0,1,0,-1,0,1,0,0,-1,0,0,1,0,0,-1,0,0,1,-1,1,0,-1,
%U A068101 0,0,0,1,0,0,-2,1,0,1,0,-1,0,0,0,1,-1,0,0,1,-1,0,0,0,0,1,-1,0,0,0,0,0,0,1,-1,0,0,1,0,1
%N A068101 a(n) = Sum_{k|n, k<=sqrt(n)} mu(k) where mu(k) is the Moebius function and the sum is over the positive divisors k of n with k <= sqrt(n).
%H A068101 Reinhard Zumkeller, <a href="/A068101/b068101.txt">Table of n, a(n) for n = 1..10000</a>
%F A068101 a(n) = Sum_{k=1..A038548(n)} A008683(A161906(n,k)). - _Reinhard Zumkeller_, Jul 30 2013
%F A068101 G.f.: Sum_{k>=1} mu(k)*x^(k^2)/(1 - x^k). - _Ilya Gutkovskiy_, Jan 03 2017
%t A068101 Table[DivisorSum[n, MoebiusMu, # <= Sqrt[n] &], {n, 103}] (* _Michael De Vlieger_, Sep 24 2017 *)
%o A068101 (Haskell)
%o A068101 a068101 = sum . map a008683 . a161906_row
%o A068101 -- _Reinhard Zumkeller_, Jul 30 2013
%o A068101 (PARI) a(n) = sumdiv(n, k, (k<=sqrt(n))*moebius(k)); \\ _Michel Marcus_, Jan 03 2017
%Y A068101 Cf. A086956.
%K A068101 sign
%O A068101 1,30
%A A068101 _Leroy Quet_, Mar 22 2002