A245838 Arithmetic derivative of (3*n + 1), n >= 1, (A016777)'.

4, 1, 7, 1, 32, 1, 13, 10, 32, 1, 19, 1, 68, 1, 25, 14, 56, 16, 31, 1, 192, 1, 59, 1, 80, 1, 43, 22, 140, 20, 49, 1, 140, 1, 55, 1, 240, 28, 61, 22, 128, 1, 101, 26, 212, 1, 73, 34, 152, 1, 113, 1, 432, 1, 85, 26, 176, 95, 91, 1, 284, 28, 143, 1, 252, 1, 103

Offset: 1

Author

Freimut Marschner, Aug 06 2014

Keywords

• nonn

Comments

Comparing A016777(n) = 3n+1 and its arithmetic derivative a(n) = (A016777(n))' allows us to select the primes in A016777, because (prime(n))' = 1.

Examples

			a(2) = (3*2 + 1)' = (7)' = 1, a(5846) = (A016777(5846))' = (3*5846 + 1)' = (17539)' = 1.
		

Links

• Freimut Marschner, Table of n, a(n) for n = 1..100000

Crossrefs

Cf. A003415 (arithmetic derivative), A016777 (3n+1), A002476 (Primes of form 6m + 1).

Programs

Maple

ad:= n -> n*add(f[2]/f[1], f=ifactors(n)[2]):
seq(ad(3*n+1), n=1..100); # Robert Israel, Aug 25 2014

PARI

a(n) = my(n=3*n+1);sum(i=1, #f=factor(n)~, n/f[1, i]*f[2, i]); \\ Michel Marcus, Aug 12 2014

Formula

a(n) = (3*n + 1)' = (A016777(n))' = A003415(A016777(n)).

Extensions

Edited: in name n>=0 replaced by n>=1. Example corrected. - Wolfdieter Lang, Oct 14 2014

Missing comma in data at a(63) inserted by Andrew Howroyd, Feb 22 2018