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A345063
a(n) = A206369(n) / gcd(A071324(n), A206369(n)).
5
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 3, 2, 1, 1, 7, 1, 1, 3, 5, 1, 5, 1, 6, 1, 1, 1, 4, 1, 1, 5, 8, 3, 21, 1, 9, 6, 5, 1, 3, 1, 1, 7, 11, 1, 11, 1, 21, 8, 1, 1, 1, 5, 15, 9, 14, 1, 3, 1, 15, 21, 1, 6, 5, 1, 1, 11, 4, 1, 5, 1, 18, 21, 1, 5, 3, 1, 11, 1, 20, 1, 2, 8, 21, 14, 5, 1, 7, 6, 1, 15, 23, 9, 21, 1, 43, 1, 1, 1, 4
OFFSET
1,10
FORMULA
a(n) = A206369(n) / A345061(n) = A206369(n) / gcd(A071324(n), A206369(n)).
MATHEMATICA
{1}~Join~Array[#2/GCD @@ {##} & @@ {Total[-#*(-1)^Range[Length[#], 1, -1]] &@ Divisors[#], Times @@ (Sum[(-1)^(#2 - k)*#1^k, {k, 0, #2}] & @@@ FactorInteger[#])} &, 101, 2] (* Michael De Vlieger, Jul 06 2021, after Amiram Eldar at A071324 and A206369 *)
PROG
(PARI)
A071324(n) = my(d=Vecrev(divisors(n))); sum(k=1, #d, (-1)^(k+1)*d[k]); \\ From A071324
A206369(n) = sumdiv(n, d, eulerphi(n/d) * issquare(d)); \\ From A206369
A345063(n) = { my(u=A206369(n)); (u/gcd(u, A071324(n))); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 07 2021
STATUS
approved