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A245838 Arithmetic derivative of (3*n + 1), n >= 1, (A016777)'. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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.

LINKS

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

FORMULA

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

EXAMPLE

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

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

PROG

(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

CROSSREFS

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

Sequence in context: A329347 A340073 A050356 * A158860 A335619 A037022

Adjacent sequences:  A245835 A245836 A245837 * A245839 A245840 A245841

KEYWORD

nonn

AUTHOR

Freimut Marschner, Aug 06 2014

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

STATUS

approved

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Last modified April 21 17:29 EDT 2021. Contains 343156 sequences. (Running on oeis4.)