

A061017


List in which n appears d(n) times, where d(n) [A000005] is the number of divisors of n.


13



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

1,2


COMMENTS

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


LINKS

Hayato Kobayashi, Perplexity on Reduced Corpora, in: Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics, Baltimore, Maryland, USA, June 2325 2014, Association for Computational Linguistics, 2014, pp. 797806.


FORMULA



EXAMPLE

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


MAPLE

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);


MATHEMATICA

Flatten[Table[Table[n, {Length[Divisors[n]]}], {n, 30}]]


PROG

(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


CROSSREFS



KEYWORD

nonn,easy


AUTHOR

Jont Allen (jba(AT)research.att.com), May 25 2001


EXTENSIONS



STATUS

approved



