A345947 a(n) = gcd(A153151(n), A344875(n)).

1, 3, 2, 7, 4, 1, 6, 15, 8, 3, 10, 1, 12, 1, 2, 31, 16, 1, 18, 1, 4, 3, 22, 1, 24, 1, 26, 3, 28, 1, 30, 63, 4, 3, 2, 7, 36, 1, 2, 3, 40, 1, 42, 1, 4, 3, 46, 1, 48, 1, 2, 3, 52, 1, 2, 5, 4, 3, 58, 1, 60, 1, 2, 127, 16, 5, 66, 1, 4, 3, 70, 1, 72, 1, 2, 3, 4, 1, 78, 1, 80, 3, 82, 1, 4, 1, 2, 3, 88, 1, 18, 7, 4, 3, 2, 1, 96

Offset: 1

Author

Antti Karttunen, Jul 01 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A153151, A344875, A345948, A345949.

Cf. also A344877, A344969, A345937.

Programs

Mathematica

Array[GCD[Which[# < 2, #, IntegerQ[Log2@ #], 2 # - 1, True, # - 1], Times @@ Map[If[#1 == 2, 2^(#2 + 1) - 1, #1^#2 - 1] & @@ # &, FactorInteger[#]]] &, 97] (* Michael De Vlieger, Jul 06 2021 *)

PARI

A153151(n) = if(!n,n,if(!bitand(n,n-1),(n+n-1),(n-1)));
A344875(n) = { my(f=factor(n)~); prod(i=1, #f, (f[1, i]^(f[2, i]+(2==f[1, i]))-1)); };
A345947(n) = gcd(A153151(n), A344875(n));

Formula

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

a(n) = A344875(n) / A345948(n).

a(n) = A153151(n) / A345949(n).

a(2n-1) = A345937(2n-1), for n >= 1.