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
The numbers in A003991 arranged in numerical order. - Matthew Vandermast, Feb 28 2003
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
N. J. A. Sloane, Table of n, a(n) for n = 1..7069
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.
FORMULA
a(n) >= pi(n+1) for all n; a(n) >= pi(n) + 1 for all n >= 24 (cf. A098357, A088526, A006218, A052511). - N. J. A. Sloane, Oct 22 2008
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/12 (A072691). - Amiram Eldar, Jan 14 2024
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
More terms from Erich Friedman, Jun 01 2001
STATUS
approved