A345949 a(n) = A153151(n) / gcd(A153151(n), A344875(n)).

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, 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, 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

Offset

1,6

Links

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

Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Formula

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

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

Mathematica

{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 *)

Prog

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

Crossrefs

Cf. A153151, A344875, A345947, A345948.

Cf. also A345939.

Sequence in context: A075463 A026518 A362394 * A379222 A348505 A051008

Adjacent sequences: A345946 A345947 A345948 * A345950 A345951 A345952

Keyword

nonn

Author

Antti Karttunen, Jul 01 2021

Status

approved