A348495 a(n) = gcd(A018804(n), A347130(n)), where A347130 is the Dirichlet convolution of the identity function with the arithmetic derivative of n (A003415), and A018804 is Pillai's arithmetical function.

1, 1, 1, 2, 1, 5, 1, 4, 3, 1, 1, 8, 1, 3, 1, 16, 1, 63, 1, 72, 5, 1, 1, 4, 5, 15, 27, 8, 1, 1, 1, 16, 7, 1, 3, 6, 1, 3, 1, 4, 1, 1, 1, 24, 9, 5, 1, 80, 7, 15, 5, 8, 1, 81, 1, 4, 1, 1, 1, 24, 1, 3, 3, 32, 9, 1, 1, 24, 1, 1, 1, 12, 1, 3, 5, 8, 3, 1, 1, 16, 27, 1, 1, 8, 11, 15, 1, 140, 1, 9, 5, 72, 1, 1, 3, 16, 1

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Formula

a(n) = gcd(A018804(n), A347130(n)).

a(n) = A003557(n) * A348496(n).

Mathematica

Table[GCD[Total@ GCD[n, Range[n]], DivisorSum[n, #*(If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]] &[n/#]) &]], {n, 97}] (* Michael De Vlieger, Oct 21 2021 *)

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A018804(n) = sumdiv(n, d, n*eulerphi(d)/d); \\ From A018804
A347130(n) = sumdiv(n, d, d*A003415(n/d));
A348495(n) = gcd(A018804(n), A347130(n));

Crossrefs

Cf. A003415, A003557, A018804, A347130, A348496.

Cf. also A348492, A348497.

Sequence in context: A161686 A289621 A069626 * A249274 A205443 A340070

Adjacent sequences: A348492 A348493 A348494 * A348496 A348497 A348498

Keyword

nonn

Author

Antti Karttunen, Oct 21 2021

Status

approved