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.

A317581 a(1) = 1; a(n > 1) = 1 + Sum_{d|n, d mu(n/d) a(d).

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%I A317581 #13 Jan 14 2022 16:03:41
%S A317581 1,0,0,1,0,2,0,0,1,2,0,-2,0,2,2,1,0,-2,0,-2,2,2,0,4,1,2,0,-2,0,-6,0,0,
%T A317581 2,2,2,7,0,2,2,4,0,-6,0,-2,-2,2,0,-4,1,-2,2,-2,0,4,2,4,2,2,0,16,0,2,
%U A317581 -2,1,2,-6,0,-2,2,-6,0,-12,0,2,-2,-2,2,-6,0,-4
%N A317581 a(1) = 1; a(n > 1) = 1 + Sum_{d|n, d<n} mu(n/d) a(d).
%C A317581 If p is prime, a(p^k) = 0 if k is odd, 1 if k is even. - _Robert Israel_, Aug 01 2018
%H A317581 Seiichi Manyama, <a href="/A317581/b317581.txt">Table of n, a(n) for n = 1..10000</a>
%p A317581 f:= n -> 1 + add(numtheory:-mobius(n/d)*procname(d),d=numtheory:-divisors(n) minus {n}):
%p A317581 f(1):= 1:
%p A317581 map(f, [$1..100]); # _Robert Israel_, Aug 01 2018
%t A317581 a[n_]:=1+Sum[MoebiusMu[n/d]*a[d],{d,Most[Divisors[n]]}];
%t A317581 Array[a,100]
%o A317581 (Python)
%o A317581 from sympy import mobius, divisors
%o A317581 def A317581(n): return 1 + (0 if n == 1 else sum(mobius(n//d)*A317581(d) for d in divisors(n,generator=True) if d < n)) # _Chai Wah Wu_, Jan 14 2022
%Y A317581 Cf. A001678, A002033, A007554, A038046, A067824.
%K A317581 sign,eigen
%O A317581 1,6
%A A317581 _Gus Wiseman_, Jul 31 2018