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

Author

Antti Karttunen, Dec 28 2020

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8191
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

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

Cf. also A160595.

Programs

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 *)

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); };

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).