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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 (list; graph; refs; listen; history; text; internal format)
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
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
a(n) = A027750(n) * A056538(n). - Charles Kusniec, Jan 21 2021
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
Cf. A000005. An inverse to A006218.
Sequence in context: A060021 A350029 A000006 * A331535 A248170 A225545
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

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Last modified May 20 03:57 EDT 2024. Contains 372703 sequences. (Running on oeis4.)