A348498 a(n) = gcd(A003415(n), A347130(n)) / A003557(n), where A003415 is the arithmetic derivative and A347130 is its Dirichlet convolution with the identity function.

0, 1, 1, 1, 1, 5, 1, 3, 1, 7, 1, 8, 1, 9, 8, 2, 1, 7, 1, 12, 10, 13, 1, 11, 1, 15, 3, 16, 1, 31, 1, 5, 14, 19, 12, 5, 1, 21, 16, 17, 1, 41, 1, 24, 13, 25, 1, 14, 1, 9, 20, 28, 1, 9, 16, 23, 22, 31, 1, 46, 1, 33, 17, 3, 18, 61, 1, 36, 26, 59, 1, 13, 1, 39, 11, 40, 18, 71, 1, 22, 2, 43, 1, 62, 22, 45, 32, 35, 1, 41

Offset

1,6

Links

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

Formula

a(n) = A348497(n) / A003557(n).

a(n) = gcd(A342001(n), A347129(n)).

Mathematica

f[n_] := If[n < 2, 0, n Total[#2/#1 & @@@ FactorInteger[n]]]; Table[GCD[f[n], DivisorSum[n, # f[n/#] &]]*Apply[Times, FactorInteger[n][[All, 1]]]/n, {n, 90}] (* 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]));
A003557(n) = (n/factorback(factorint(n)[, 1]));
A347130(n) = sumdiv(n, d, d*A003415(n/d));
A348498(n) = (gcd(A003415(n), A347130(n))/A003557(n));

Crossrefs

Cf. A003415, A003557, A342001, A347129, A347130, A348497, A348502 [= a(A276086(n))].

Cf. also A348494, A348496.

Sequence in context: A327921 A155059 A347964 * A206076 A329374 A115638

Adjacent sequences: A348495 A348496 A348497 * A348499 A348500 A348501

Keyword

nonn

Author

Antti Karttunen, Oct 23 2021

Status

approved