A348492 Greatest common divisor of the arithmetic derivative (A003415) and Pillai's arithmetical function (A018804).

1, 1, 1, 4, 1, 5, 1, 4, 3, 1, 1, 8, 1, 3, 1, 16, 1, 21, 1, 24, 5, 1, 1, 4, 5, 15, 27, 8, 1, 1, 1, 16, 7, 1, 3, 12, 1, 3, 1, 4, 1, 1, 1, 24, 3, 5, 1, 16, 7, 15, 5, 8, 1, 81, 1, 4, 1, 1, 1, 4, 1, 3, 3, 64, 9, 1, 1, 24, 1, 1, 1, 12, 1, 3, 5, 8, 3, 1, 1, 16, 27, 1, 1, 4, 11, 15, 1, 140, 1, 3, 5, 24, 1, 1, 3, 16, 1, 7

Offset

1,4

Links

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

Formula

a(n) = gcd(A003415(n), A018804(n)).

For n > 1, a(n) = A003415(n) / A348493(n).

a(n) = A003557(n) * A348494(n).

Mathematica

Array[GCD[Total@ GCD[#, Range[#]], # Total[#2/#1 & @@@ FactorInteger[#]]] &, 98] (* 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
A348492(n) = gcd(A003415(n), A018804(n));

Crossrefs

Cf. A003415, A003557, A018804, A348493, A348494.

Cf. also A342413, A342458, A348495.

Sequence in context: A143313 A132588 A195986 * A353576 A046785 A060044

Adjacent sequences: A348489 A348490 A348491 * A348493 A348494 A348495

Keyword

nonn

Author

Antti Karttunen, Oct 21 2021

Status

approved