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%I #14 Oct 01 2023 02:40:03
%S 1,1,2,1,2,2,2,1,1,2,2,2,2,2,4,1,2,1,2,2,4,2,2,2,1,2,4,2,2,4,2,1,4,2,
%T 4,1,2,2,4,2,2,4,2,2,2,2,2,2,1,1,4,2,2,4,4,2,4,2,2,4,2,2,2,1,4,4,2,2,
%U 4,4,2,1,2,2,2,2,4,4,2,2,1,2,2,4,4,2,4,2,2,2,4,2,4,2,4,2,2,1,2,1,2,4,2,2,8
%N a(n) = gcd(2^n, sigma(2,n)) = gcd(A000079(n), A001157(n)).
%H Antti Karttunen, <a href="/A082902/b082902.txt">Table of n, a(n) for n = 1..65537</a>
%F a(n) = A006519(A001157(n)). - _Antti Karttunen_, Sep 27 2018
%F Multiplicative with a(2^e) = 1, and a(p^e) = A006519(e+1) for an odd prime p. - _Amiram Eldar_, Oct 01 2023
%t a[n_] := 2^IntegerExponent[DivisorSigma[2, n], 2]; Array[a, 100] (* _Amiram Eldar_, Oct 01 2023 *)
%o (PARI) A082902(n) = gcd(2^n, sigma(n, 2)); \\ _Antti Karttunen_, Sep 27 2018
%Y Cf. A000079, A001157, A006519.
%K nonn,mult
%O 1,3
%A _Labos Elemer_, Apr 22 2003
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