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A061017
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List in which n appears d(n) times, where d(n) [A000005] is the number of divisors of n.
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13
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1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 24
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OFFSET
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1,2
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COMMENTS
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The union of N, 2N, 3N, ..., where N = {1, 2, 3, 4, 5, 6, ...}. In other words, the numbers {m*n, m >= 1, n >= 1} sorted into nondecreasing order.
Considering the maximal rectangle in each of the Ferrers graphs of partitions of n, a(n) is the smallest such maximal rectangle; a(n) is also an inverse of A006218. - Henry Bottomley, Mar 11 2002
Least k such that tau(1) + tau(2) + tau(3) + ... + tau(k) >= n. - Michel Lagneau, Jan 04 2012
The number 1 appears only once, primes appear twice, squares of primes appear thrice. All other positive integers appear at least four times. - Alonso del Arte, Nov 24 2013
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LINKS
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Hayato Kobayashi, Perplexity on Reduced Corpora, in: Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics, Baltimore, Maryland, USA, June 23-25 2014, Association for Computational Linguistics, 2014, pp. 797-806.
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FORMULA
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EXAMPLE
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Array begins:
1
2 2
3 3
4 4 4
5 5
6 6 6 6
7 7
8 8 8 8
9 9 9
10 10 10 10
11 11
12 12 12 12 12 12
13 13
14 14 14 14
15 15 15 15
16 16 16 16 16
17 17
18 18 18 18 18 18
19 19
20 20 20 20 20 20
21 21 21 21
22 22 22 22
23 23
24 24 24 24 24 24 24 24
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MAPLE
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with(numtheory); t1:=[]; for i from 1 to 1000 do for j from 1 to tau(i) do t1:=[op(t1), i]; od: od: t1:=sort(t1);
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MATHEMATICA
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Flatten[Table[Table[n, {Length[Divisors[n]]}], {n, 30}]]
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PROG
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(PARI) a(n)=if(n<0, 0, t=1; while(sum(k=1, t, floor(t/k))<n, t++); t) \\ Benoit Cloitre, Nov 08 2009
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Jont Allen (jba(AT)research.att.com), May 25 2001
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EXTENSIONS
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STATUS
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approved
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