A270807 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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