A348493 a(n) = A003415(n) / gcd(A003415(n), A018804(n)), where A003415 is the arithmetic derivative and A018804 is Pillai's arithmetical function.

0, 1, 1, 1, 1, 1, 1, 3, 2, 7, 1, 2, 1, 3, 8, 2, 1, 1, 1, 1, 2, 13, 1, 11, 2, 1, 1, 4, 1, 31, 1, 5, 2, 19, 4, 5, 1, 7, 16, 17, 1, 41, 1, 2, 13, 5, 1, 7, 2, 3, 4, 7, 1, 1, 16, 23, 22, 31, 1, 23, 1, 11, 17, 3, 2, 61, 1, 3, 26, 59, 1, 13, 1, 13, 11, 10, 6, 71, 1, 11, 4, 43, 1, 31, 2, 3, 32, 1, 1, 41, 4, 4, 34, 49, 8

Offset

1,8

Links

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

Formula

a(n) = A003415(n) / A348492(n).

Mathematica

Array[#2/GCD[#1, #2] & @@ {Total@ GCD[#, Range[#]], If[# < 2, 0, # Total[#2/#1 & @@@ FactorInteger[#]]]} &, 95] (* 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
A348493(n) = { my(u=A003415(n)); (u/gcd(u, A018804(n))); };

Crossrefs

Cf. A003415, A018804, A348492, A348494.

Sequence in context: A019971 A330501 A010606 * A317919 A255820 A318436

Adjacent sequences: A348490 A348491 A348492 * A348494 A348495 A348496

Keyword

nonn

Author

Antti Karttunen, Oct 21 2021

Status

approved