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A361023
a(n) = 1 if A007814(sigma(n)) >= A007814(n), otherwise 0, where A007814(n) gives the 2-adic valuation of n.
3
1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1
OFFSET
1
COMMENTS
Parity of A017666(n), the denominator of sigma(n)/n (the abundancy index of n).
FORMULA
a(n) = [A336937(n) >= A007814(n)] = [A361025(n) > 0], where [ ] is the Iverson bracket.
a(n) = A324903(n) + A361024(n).
a(n) = A000035(A017666(n)) = A000035(n / gcd(sigma(n), n)).
MATHEMATICA
a[n_] := Mod[Denominator[DivisorSigma[-1, n]], 2]; Array[a, 100] (* Amiram Eldar, Mar 03 2023 *)
PROG
(PARI) A361023(n) = (valuation(sigma(n), 2)>=valuation(n, 2));
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 03 2023
STATUS
approved