A340085 a(n) = A336466(n) / gcd(n-1, A336466(n)); Odd part of A340082(n).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 3, 5, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 5, 1, 3, 1, 1, 9, 3, 1, 1, 3, 1, 5, 1, 11, 1, 1, 3, 1, 1, 1, 1, 1, 5, 3, 9, 7, 1, 1, 1, 15, 3, 1, 3, 1, 1, 1, 11, 1, 1, 1, 1, 9, 1, 3, 15, 3, 1, 1, 1, 5, 1, 3, 1, 21, 7, 5, 1, 1, 1, 11, 15, 23, 9, 1, 1, 9, 5, 1, 1, 1, 1, 3, 3

Offset

1,14

Links

Antti Karttunen, Table of n, a(n) for n = 1..8191

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

Formula

a(n) = A000265(A340082(n)).

a(n) = A336466(n) / A340084(n) = A336466(n) / gcd(n-1, A336466(n)).

For all n >= 0, a(A003961(A019565(n))) = a(A019565(2*n)) = A339901(n).

Mathematica

Array[#2/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])); };
A340085(n) = { my(u=A336466(n)); u/gcd(n-1, u); };

Crossrefs

Cf. A000265, A003958, A003961, A019565, A336466, A339901, A340082, A340084, A340086.

Cf. also A160595.

Sequence in context: A001165 A137420 A134866 * A143261 A204116 A093421

Adjacent sequences: A340082 A340083 A340084 * A340086 A340087 A340088

Keyword

nonn

Author

Antti Karttunen, Dec 28 2020

Status

approved