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

1,2

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

Prog

(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
(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

Crossrefs

Cf. A006530, A269304, A271418.

For first differences see A270808.

Sequence in context: A338129 A327573 A306069 * A157048 A190857 A003543

Adjacent sequences: A270804 A270805 A270806 * A270808 A270809 A270810

Keyword

nonn

Author

N. J. A. Sloane, Apr 05 2016

Status

approved