A342014 Arithmetic derivative of n, taken modulo n: a(n) = A003415(n) mod n.

0, 1, 1, 0, 1, 5, 1, 4, 6, 7, 1, 4, 1, 9, 8, 0, 1, 3, 1, 4, 10, 13, 1, 20, 10, 15, 0, 4, 1, 1, 1, 16, 14, 19, 12, 24, 1, 21, 16, 28, 1, 41, 1, 4, 39, 25, 1, 16, 14, 45, 20, 4, 1, 27, 16, 36, 22, 31, 1, 32, 1, 33, 51, 0, 18, 61, 1, 4, 26, 59, 1, 12, 1, 39, 55, 4, 18, 71, 1, 16, 27, 43, 1, 40, 22, 45, 32, 52, 1, 33

Offset: 1

Author

Antti Karttunen, Mar 04 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A003415, A072873 (positions of zeros), A085731 [= gcd(n, a(n))], A342015 [= A342014(A276086(n))].

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A342014(n) = (A003415(n)%n);

Formula

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