

A085790


Integers sorted by the sum of their divisors.


10



1, 2, 3, 5, 4, 7, 6, 11, 9, 13, 8, 10, 17, 19, 14, 15, 23, 12, 29, 16, 25, 21, 31, 22, 37, 18, 27, 20, 26, 41, 43, 33, 35, 47, 34, 53, 28, 39, 49, 24, 38, 59, 61, 32, 67, 30, 46, 51, 55, 71, 73, 45, 57, 79, 44, 65, 83, 40, 58, 89, 36, 50, 42, 62, 69, 77, 52, 97, 101, 63, 103, 85
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OFFSET

1,2


COMMENTS

Integers having the same sum of divisors are sorted in ascending order, e.g., sigma(14)=sigma(15)=sigma(23)=24 > a(15)=14, a(16)=15, a(17)=23.
Also an irregular triangle where the kth row consists of all numbers with divisor sum k. See A054973(k) for the kth row length.  Jeppe Stig Nielsen, Jan 29 2015
By definition this is a permutation of the positive integers. Also positive integers of A299762.  Omar E. Pol, Mar 14 2018


LINKS

Hugo Pfoertner, Table of n, a(n) for n=1..10000
Jeppe Stig Nielsen, First 10000 rows of the triangle for a(n)
Index entries for sequences that are permutations of the natural numbers


EXAMPLE

a(9)=9, a(10)=13, a(11)=8 because sigma(9)=13=9+3+1, sigma(13)=14=13+1,
sigma(8)=15=8+4+2+1 and there are no other numbers with those sigma values.
Irregular triangle starts (row numbers to the left of colons are not part of this sequence):
1: 1,
2:
3: 2,
4: 3,
5:
6: 5,
7: 4,
8: 7,
9:
10:
11:
12: 6, 11,
13: 9,
14: 13,
15: 8,
16:
17:
18: 10, 17,
19:
20: 19,
21:
22:
23:
24: 14, 15, 23,
25:
 Jeppe Stig Nielsen, Feb 02 2015


CROSSREFS

Cf. A000203 (sigma(n)), A007609 (values taken by sigma(n), sorted), A002191 (possible values for sigma(n)), A002192 (first column).
Cf. A152454 (similar sequence for proper divisors only (aliquot parts)).
Sequence in context: A282649 A102454 A232640 * A257339 A210882 A117120
Adjacent sequences: A085787 A085788 A085789 * A085791 A085792 A085793


KEYWORD

easy,nonn,tabf


AUTHOR

Hugo Pfoertner, Jul 23 2003


STATUS

approved



