A369049 a(n) = n mod n', where n' is the arithmetic derivative of n, A003415.

0, 0, 0, 0, 1, 0, 8, 3, 3, 0, 12, 0, 5, 7, 16, 0, 18, 0, 20, 1, 9, 0, 24, 5, 11, 0, 28, 0, 30, 0, 32, 5, 15, 11, 36, 0, 17, 7, 40, 0, 1, 0, 44, 6, 21, 0, 48, 7, 5, 11, 52, 0, 54, 7, 56, 13, 27, 0, 60, 0, 29, 12, 64, 11, 5, 0, 68, 17, 11, 0, 72, 0, 35, 20, 76, 5, 7, 0, 80, 81, 39, 0, 84, 19, 41, 23, 88, 0, 90, 11

Offset: 2

Author

Antti Karttunen, Jan 15 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 2..65537

Crossrefs

Cf. A003415, A085731 [= gcd(A003415(n), a(n))].

Cf. also A328382, A342014, A369050.

Programs

Mathematica

Array[Mod[#, #  Total[#2/#1 & @@@ FactorInteger[#]]] &, 120, 2] (* Michael De Vlieger, Jan 15 2024 *)

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A369049(n) = (n % A003415(n));

Formula

a(n) = n mod A003415(n).