A345062 a(n) = A071324(n) / gcd(A071324(n), A206369(n)).

1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 4, 1, 4, 3, 1, 1, 13, 1, 1, 4, 6, 1, 8, 1, 7, 1, 1, 1, 11, 1, 1, 6, 9, 4, 25, 1, 10, 7, 6, 1, 8, 1, 1, 9, 12, 1, 16, 1, 31, 9, 1, 1, 2, 6, 19, 10, 15, 1, 5, 1, 16, 23, 1, 7, 12, 1, 1, 12, 7, 1, 7, 1, 19, 31, 1, 6, 7, 1, 12, 1, 21, 1, 3, 9, 22, 15, 6, 1, 17, 7, 1, 16, 24, 10, 32, 1, 57

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..14161

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

Formula

a(n) = A071324(n) / A345061(n) = A071324(n) / gcd(A071324(n), A206369(n)).

Mathematica

{1}~Join~Array[#1/GCD @@ {##} & @@ {Total[-#*(-1)^Range[Length[#], 1, -1]] &@ Divisors[#], Times @@ (Sum[(-1)^(#2 - k)*#1^k, {k, 0, #2}] & @@@ FactorInteger[#])} &, 97, 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
A345062(n) = { my(u=A071324(n)); (u/gcd(u, A206369(n))); };

Crossrefs

Cf. A071324, A206369, A345060, A345061, A345063, A345064.

Sequence in context: A060246 A161204 A123541 * A324537 A090379 A254655

Adjacent sequences: A345059 A345060 A345061 * A345063 A345064 A345065

Keyword

nonn

Author

Antti Karttunen, Jun 07 2021

Status

approved