cp's OEIS Frontend

A346202 a(n) = L(n)^2, where L is Liouville's function.

%I A346202 #35 Dec 21 2022 04:49:10
%S A346202 1,0,1,0,1,0,1,4,1,0,1,4,9,4,1,0,1,4,9,16,9,4,9,4,1,0,1,4,9,16,25,36,
%T A346202 25,16,9,4,9,4,1,0,1,4,9,16,25,16,25,36,25,36,25,36,49,36,25,16,9,4,9,
%U A346202 4,9,4,9,4,1,4,9,16,9,16,25,36,49,36,49,64,49
%N A346202 a(n) = L(n)^2, where L is Liouville's function.
%C A346202 The Riemann Hypothesis is equivalent to the statement that, for every fixed eps > 0, lim_{n->oo} (L(n) / n^(eps + 1/2)) = 0.
%D A346202 Peter Borwein, Stephen Choi, Brendan Rooney, and Andrea Weirathmueller, The Riemann Hypothesis: A Resource for the Afficionado and Virtuoso Alike, 2007, page 6, Theorem 1.2.
%F A346202 a(n) = Sum_{i=1..n} Sum_{j=1..n} A008836(i)*A008836(j).
%F A346202 a(n) = A002819(n)^2. - _Ilya Gutkovskiy_, Jul 10 2021
%p A346202 L:= proc(n) option remember; `if`(n<1, 0,
%p A346202      (-1)^numtheory[bigomega](n)+L(n-1))
%p A346202     end:
%p A346202 a:= n-> L(n)^2:
%p A346202 seq(a(n), n=1..77);  # _Alois P. Heinz_, Jul 28 2021
%t A346202 Table[Sum[LiouvilleLambda[n], {n, 1, nn}]^2, {nn, 1, 77}]
%o A346202 (PARI) a008836(n) = (-1)^bigomega(n) \\ after _Charles R Greathouse IV_ in A008836
%o A346202 a(n) = sum(i=1, n, sum(j=1, n, a008836(i)*a008836(j))) \\ _Felix Fröhlich_, Jul 10 2021
%o A346202 (Python)
%o A346202 from functools import reduce
%o A346202 from operator import ixor
%o A346202 from sympy import factorint
%o A346202 def A346202(n): return sum(-1 if reduce(ixor, factorint(i).values(),0)&1 else 1 for i in range(1,n+1))**2 # _Chai Wah Wu_, Dec 20 2022
%Y A346202 Cf. A002819, A008836, A028488 (positions of zeros).
%K A346202 nonn
%O A346202 1,8
%A A346202 _Mats Granvik_, Jul 10 2021