A270807 Trajectory of 1 under the map n -> n + n/gpf(n) + 1 (see A269304).

1, 3, 5, 7, 9, 13, 15, 19, 21, 25, 31, 33, 37, 39, 43, 45, 55, 61, 63, 73, 75, 91, 99, 109, 111, 115, 121, 133, 141, 145, 151, 153, 163, 165, 181, 183, 187, 199, 201, 205, 211, 213, 217, 225, 271, 273, 295, 301, 309, 313, 315, 361, 381, 385, 421, 423, 433, 435, 451, 463, 465

Offset: 1

Author

N. J. A. Sloane, Apr 05 2016

Keywords

• nonn

Comments

Cody M. Haderlie (see A269304) conjectures that the trajectory of any initial value will eventually merge with this sequence. The trajectory of 2, for example, begins 2, 4, 7, 9, 13, 15, 19, 21, 25, ... and from 7 on coincides with this sequence. See A271418.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006530, A269304, A271418.

For first differences see A270808.

Programs

PARI

gpf(n) = if (n==1, 1, vecmax(factor(n)[,1]));
lista(nn) = {a = 1; for (n=1, nn, print1(a, ", "); a = a + a/gpf(a) + 1;);} \\ Michel Marcus, Apr 06 2016

Python

from _future_ import division
from sympy import primefactors
A270807_list, b = [], 1
for i in range(10000):
    A270807_list.append(b)
    b += b//(max(primefactors(b)+[1])) + 1 # Chai Wah Wu, Apr 06 2016