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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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7
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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 (se16(AT)btinternet.com), Mar 11 2002
The numbers in A003991 arranged in numerical order. - Matthew Vandermast (ghodges14(AT)comcast.net), Feb 28 2003
Least k such that tau(1)+tau(2)+tau(3)+...+tau(k) >= n. - Michel Lagneau, Jan 04 2012
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LINKS
| N. J. A. Sloane, Table of n, a(n) for n = 1..7069
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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 (njas(AT)research.att.com), Oct 22 2008
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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);
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MATHEMATICA
| Flatten[Table[Table[n, {Length[Divisors[n]]}], {n, 1, 30}]]
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PROG
| (PARI) a(n)=if(n<0, 0, t=1; while(sum(k=1, t, floor(t/k))<n, t++); t) [From Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 08 2009]
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CROSSREFS
| Cf. A000005. An inverse to A006218.
Sequence in context: A024417 A060021 A000006 * A088462 A189574 A093337
Adjacent sequences: A061014 A061015 A061016 * A061018 A061019 A061020
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KEYWORD
| nonn,easy
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AUTHOR
| Jont Allen (jba(AT)research.att.com), May 25 2001
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EXTENSIONS
| More terms from Erich Friedman (efriedma(AT)stetson.edu), Jun 01 2001
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