A331694 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.

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, 42, 40, 42, 30, 46, 32, 63, 48, 54, 48, 67, 38, 60, 56, 60, 42, 48, 44, 84, 60, 72, 48, 54, 57, 93, 72, 98, 54, 60, 72, 106, 80, 90, 60, 66, 62, 96, 86, 127, 84, 72

Offset

1,2

Comments

This sequence has similarities with A084110.

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

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Formula

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

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

Example

For n = 30:
- we have:
  k  e_k  d_k
  -  ---  ---
  0    0  N/A
  1    1    1
  2    3    2
  3    0    3
  4    5    5
  5   11    6
  6    1   10
  7   16   15
  8   46   30
- so a(30) = 46.

Prog

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

Crossrefs

Cf. A027750, A084110, A071324.

Sequence in context: A187793 A284326 A117553 * A290270 A168275 A325968

Adjacent sequences: A331691 A331692 A331693 * A331695 A331696 A331697

Keyword

nonn

Author

Rémy Sigrist, Jan 25 2020

Status

approved