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A085790
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Integers sorted by the sum of their divisors.
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16
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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
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1,2
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COMMENTS
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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 k-th row consists of all numbers with divisor sum k. See A054973(k) for the k-th 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
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LINKS
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EXAMPLE
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a(9) = 9, a(10) = 13, a(11) = 8 because sigma(9) = 9 + 3 + 1 = 13, sigma(13) = 13 + 1 = 14, sigma(8) = 8 + 4 + 2 + 1 = 15 and there are no other numbers with those sigma values.
Irregular triangle starts: (row numbers to the left are not part of the sequence)
n : row(n)
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 :
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PROG
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(PARI) A085790_row(n)=invsigma(n) \\ Cf. Alekseyev link for invsigma(). - M. F. Hasler, Nov 21 2019
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CROSSREFS
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Cf. A152454 (similar sequence for proper divisors only (aliquot parts)).
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KEYWORD
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easy,nonn,tabf
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AUTHOR
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STATUS
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approved
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