A331694 - OEIS

%I #13 Jan 28 2020 12:47:04

%S 1,3,4,7,6,6,8,15,13,18,12,22,14,24,24,31,18,33,20,32,32,36,24,38,31,

%T 42,40,42,30,46,32,63,48,54,48,67,38,60,56,60,42,48,44,84,60,72,48,54,

%U 57,93,72,98,54,60,72,106,80,90,60,66,62,96,86,127,84,72

%N For any n > 0, let d_1, ..., d_k be the divisors of n, in ascending order; set e_0 = 0 and for i = 1..k, if e_{i-1} >= d_i then set e_i = e_{i-1} - d_i else set e_i = e_{i-1} + d_i; a(n) = e_k.

%C This sequence has similarities with A084110.

%C Fixed points appear to be sparse; the first few are 1, 6, 126, 198, 1433322, 317533782, 386625738, 451240398.

%H Rémy Sigrist, <a href="/A331694/b331694.txt">Table of n, a(n) for n = 1..10000</a>

%F a(p^k) = (p^(k+1)-1)/(p-1) for any k >= 0 and any prime number p.

%F n <= a(n) < 2*n.

%e For n = 30:

%e - we have:

%e   k  e_k  d_k

%e   -  ---  ---

%e   0    0  N/A

%e   1    1    1

%e   2    3    2

%e   3    0    3

%e   4    5    5

%e   5   11    6

%e   6    1   10

%e   7   16   15

%e   8   46   30

%e - so a(30) = 46.

%o (PARI) a(n) = my (e=0); fordiv (n, d, if (e>=d, e-=d, e+=d)); e

%Y Cf. A027750, A084110, A071324.

%K nonn

%O 1,2

%A _Rémy Sigrist_, Jan 25 2020