A345948 a(n) = A344875(n) / gcd(A153151(n), A344875(n)).

1, 1, 1, 1, 1, 6, 1, 1, 1, 4, 1, 14, 1, 18, 4, 1, 1, 24, 1, 28, 3, 10, 1, 30, 1, 36, 1, 14, 1, 24, 1, 1, 5, 16, 12, 8, 1, 54, 12, 20, 1, 36, 1, 70, 8, 22, 1, 62, 1, 72, 16, 28, 1, 78, 20, 18, 9, 28, 1, 56, 1, 90, 24, 1, 3, 12, 1, 112, 11, 24, 1, 120, 1, 108, 24, 42, 15, 72, 1, 124, 1, 40, 1, 84, 16, 126, 28, 50, 1, 96, 4, 22

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

a(2n-1) = A345938(2n-1), for all n >= 1.

Mathematica

{1}~Join~Array[#2/GCD @@ {##} & @@ {Which[# < 2, #, IntegerQ[Log2@ #], 2 # - 1, True, # - 1], Times @@ Map[If[#1 == 2, 2^(#2 + 1) - 1, #1^#2 - 1] & @@ # &, FactorInteger[#]]} &, 91, 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)); };
A345948(n) = { my(u=A344875(n)); (u/gcd(A153151(n), u)); };

Crossrefs

Cf. A153151, A344875, A345947, A345949.

Cf. also A345938.

Sequence in context: A355925 A275109 A331735 * A346013 A344697 A364917

Adjacent sequences: A345945 A345946 A345947 * A345949 A345950 A345951

Keyword

nonn

Author

Antti Karttunen, Jul 01 2021

Status

approved