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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 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 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))

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