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A340084
a(n) = gcd(n-1, A336466(n)); Odd part of A340081(n).
4
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
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); };
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 29 2020
STATUS
approved