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

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

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

Formula

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

Prog

(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);

Crossrefs

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

Sequence in context: A216157 A216851 A179290 * A355953 A167864 A232809

Adjacent sequences: A342011 A342012 A342013 * A342015 A342016 A342017

Keyword

nonn

Author

Antti Karttunen, Mar 04 2021

Status

approved