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a(n) = A153151(n) / gcd(A153151(n), A344875(n)).
4

%I #13 Jul 06 2021 20:18:46

%S 1,1,1,1,1,5,1,1,1,3,1,11,1,13,7,1,1,17,1,19,5,7,1,23,1,25,1,9,1,29,1,

%T 1,8,11,17,5,1,37,19,13,1,41,1,43,11,15,1,47,1,49,25,17,1,53,27,11,14,

%U 19,1,59,1,61,31,1,4,13,1,67,17,23,1,71,1,73,37,25,19,77,1,79,1,27,1,83,21,85,43,29,1,89,5,13,23

%N a(n) = A153151(n) / gcd(A153151(n), A344875(n)).

%H Antti Karttunen, <a href="/A345949/b345949.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A345949/a345949.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%F a(n) = A153151(n) / A345947(n) = A153151(n) / gcd(A153151(n), A344875(n)).

%F a(2n-1) = A345939(2n-1), for n > 1.

%t {1}~Join~Array[#1/GCD @@ {##} & @@ {Which[# < 2, #, IntegerQ[Log2@ #], 2 # - 1, True, # - 1], Times @@ Map[If[#1 == 2, 2^(#2 + 1) - 1, #1^#2 - 1] & @@ # &, FactorInteger[#]]} &, 92, 2] (* _Michael De Vlieger_, Jul 06 2021 *)

%o (PARI)

%o A153151(n) = if(!n,n,if(!bitand(n,n-1),(n+n-1),(n-1)));

%o A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };

%o A345949(n) = { my(u=A153151(n)); (u/gcd(u, A344875(n))); };

%Y Cf. A153151, A344875, A345947, A345948.

%Y Cf. also A345939.

%K nonn

%O 1,6

%A _Antti Karttunen_, Jul 01 2021