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

2,7

Links

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

Formula

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

Mathematica

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

Prog

(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));

Crossrefs

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

Cf. also A328382, A342014, A369050.

Sequence in context: A100863 A021986 A197729 * A010148 A246822 A168356

Adjacent sequences: A369046 A369047 A369048 * A369050 A369051 A369052

Keyword

nonn

Author

Antti Karttunen, Jan 15 2024

Status

approved