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a(n) = 1 if sigma(n) has an odd number of prime factors (with multiplicity), and 0 otherwise. Here sigma is the sum of divisors function.
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%I #11 May 15 2022 17:21:12

%S 0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,1,0,

%T 1,0,0,0,0,0,1,0,1,0,1,1,1,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0,

%U 0,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,0,1,1,1,1,0,0,1,0,0,0,1

%N a(n) = 1 if sigma(n) has an odd number of prime factors (with multiplicity), and 0 otherwise. Here sigma is the sum of divisors function.

%C Parity of A058063(n), bigomega(sigma(n)).

%H Antti Karttunen, <a href="/A353810/b353810.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%F a(n) = A066829(A000203(n)) = A000035(A058063(n)) = A000035(A001222(A000203(n))).

%t a[n_] := If[OddQ[PrimeOmega[DivisorSigma[1, n]]], 1, 0]; Array[a, 100] (* _Amiram Eldar_, May 13 2022 *)

%o (PARI) A353810(n) = (bigomega(sigma(n))%2);

%Y Cf. A000035, A000203, A001222, A058063, A066829, A353811.

%K nonn

%O 1

%A _Antti Karttunen_, May 13 2022