A345063 - OEIS

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A345063

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

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,10

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) = 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

Cf. A071324, A206369, A345060, A345061, A345062, A345064.

Sequence in context: A104984 A083868 A128199 * A337216 A249617 A304091

Adjacent sequences: A345060 A345061 A345062 * A345064 A345065 A345066

KEYWORD

nonn

AUTHOR

Antti Karttunen, Jun 07 2021

STATUS

approved