A340084 a(n) = gcd(n-1, A336466(n)); Odd part of A340081(n).

1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 3, 1, 1, 1, 1, 1, 9, 1, 1, 1, 11, 1, 1, 1, 1, 3, 7, 1, 15, 1, 1, 1, 1, 1, 9, 1, 1, 1, 5, 1, 21, 1, 1, 1, 23, 1, 3, 1, 1, 3, 13, 1, 1, 1, 1, 1, 29, 1, 15, 1, 1, 1, 1, 5, 33, 1, 1, 3, 35, 1, 9, 1, 1, 3, 1, 1, 39, 1, 1, 1, 41, 1, 1, 1, 1, 1, 11, 1, 9, 1, 1, 1, 1, 1, 3, 1, 1, 1, 25, 1, 51, 1, 1

Offset

1,7

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) = gcd(n-1, A336466(n)).

a(n) = A000265(A340081(n)) = A336466(n) / A340085(n).

For n >= 2, a(n) = A000265(n-1) / A340086(n).

For n >= 1, a(A000040(n)) = A057023(n).

For n >= 0, a(A019565(2*n)) = A339899(n).

Mathematica

Array[GCD[#1 - 1, #2] & @@ {#, Times @@ Map[If[# <= 2, 1, (# - 1)/2^IntegerExponent[# - 1, 2]] &, Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[#]]]} &, 105] (* Michael De Vlieger, Dec 29 2020 *)

Prog

(PARI)
A000265(n) = (n>>valuation(n, 2));
A336466(n) = { my(f=factor(n)); prod(k=1, #f~, if(2==f[k, 1], 1, (A000265(f[k, 1]-1))^f[k, 2])); };
A340084(n) = { my(u=A336466(n)); gcd(n-1, u); };

Crossrefs

Cf. A000265, A003958, A003961, A019565, A057023, A336466, A339899, A340081, A340085, A340086.

Cf. also A049559.

Sequence in context: A101021 A357990 A346485 * A317939 A086767 A119288

Adjacent sequences: A340081 A340082 A340083 * A340085 A340086 A340087

Keyword

nonn

Author

Antti Karttunen, Dec 29 2020

Status

approved