A348497 a(n) = gcd(A003415(n), A347130(n)), where A003415 is the arithmetic derivative and A347130 is its Dirichlet convolution with the identity function.

0, 1, 1, 2, 1, 5, 1, 12, 3, 7, 1, 16, 1, 9, 8, 16, 1, 21, 1, 24, 10, 13, 1, 44, 5, 15, 27, 32, 1, 31, 1, 80, 14, 19, 12, 30, 1, 21, 16, 68, 1, 41, 1, 48, 39, 25, 1, 112, 7, 45, 20, 56, 1, 81, 16, 92, 22, 31, 1, 92, 1, 33, 51, 96, 18, 61, 1, 72, 26, 59, 1, 156, 1, 39, 55, 80, 18, 71, 1, 176, 54, 43, 1, 124, 22, 45

Offset

1,4

Links

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

Formula

a(n) = gcd(A003415(n), A347130(n)).

a(n) = A003557(n) * A348498(n).

Mathematica

f[n_] := If[n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[n]]]; Table[GCD[f[n], DivisorSum[n, # f[n/#] &]], {n, 86}] (* Michael De Vlieger, Oct 25 2021 *)

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A347130(n) = sumdiv(n, d, d*A003415(n/d));
A348497(n) = gcd(A003415(n), A347130(n));

Crossrefs

Cf. A003415, A003557, A347130, A348498.

Cf. also A348492, A348495.

Sequence in context: A119763 A363087 A092142 * A376021 A299161 A327249

Adjacent sequences: A348494 A348495 A348496 * A348498 A348499 A348500

Keyword

nonn

Author

Antti Karttunen, Oct 23 2021

Status

approved