A348493 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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]));