

A061017


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


10



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
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


REFERENCES

Hayato Kobayashi, Perplexity on Reduced Corpora; http://hayatokobayashi.com/paper/ACL2014_Kobayashi.pdf, 2014.


LINKS

N. J. A. Sloane, Table of n, a(n) for n = 1..7069


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


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: A024417 A060021 A000006 * A225545 A088462 A189574
Adjacent sequences: A061014 A061015 A061016 * A061018 A061019 A061020


KEYWORD

nonn,easy,changed


AUTHOR

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


EXTENSIONS

More terms from Erich Friedman, Jun 01 2001


STATUS

approved



