A340085 - OEIS

%I #11 Dec 29 2020 20:37:56

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A340085/b340085.txt">Table of n, a(n) for n = 1..8191</a>

%H Antti Karttunen, <a href="/A340085/a340085.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

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

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

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

%t 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 *)

%o (PARI)

%o A000265(n) = (n>>valuation(n,2));

%o A336466(n) = { my(f=factor(n)); prod(k=1,#f~,if(2==f[k,1],1,(A000265(f[k,1]-1))^f[k,2])); };

%o A340085(n) = { my(u=A336466(n)); u/gcd(n-1, u); };

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

%Y Cf. also A160595.

%K nonn

%O 1,14

%A _Antti Karttunen_, Dec 28 2020