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 A064364 Positive integers sorted by A001414(n), the sum of their prime divisors, as the major key and n as the minor key. 8
 1, 2, 3, 4, 5, 6, 8, 9, 7, 10, 12, 15, 16, 18, 14, 20, 24, 27, 21, 25, 30, 32, 36, 11, 28, 40, 45, 48, 54, 35, 42, 50, 60, 64, 72, 81, 13, 22, 56, 63, 75, 80, 90, 96, 108, 33, 49, 70, 84, 100, 120, 128, 135, 144, 162, 26, 44, 105, 112, 125, 126, 150, 160, 180, 192, 216, 243 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This is a permutation of the positive integers. a(1) could be taken as 0 because 1 is not a member of A001414 and one could start with a(0)=1 (see the W. Lang link). The row length sequence of this array is A000607(n), n>=2. If the array is [1,0,2,3,4,5,6,6,...] with offset 0 then the row length sequence is A000607(n), n>=0. From David James Sycamore, May 11 2018: (Start) For n>1 a(n) is the smallest number not yet seen such that Sopfr(a(n)) is the least possible integer >= Sopfr(a(n-1)). The sequence lists consecutively, elements of the finite ordered sets S(k)={x: Sopfr(x) = k; k>=2}. When a(n) = A056240(k) for some k>=2 then Sopfr(n) = k and a(n) is the first of A000607(k) successive terms, all of which have Sopfr = k. Consequently the sequence follows a sawtooth profile, rising from a(n) = A056240(k) to A000792(k), the greatest number whose Sopfr is k, then falling abruptly as k indexes to k+1. (End) LINKS Reinhard Zumkeller and Alois P. Heinz, Rows n = 1..60, flattened (first 32 rows from Reinhard Zumkeller) H. Havermann: The first 100 sums (complete, a 6 MB file) W. Lang, First 16 rows. EXAMPLE The triangle reads: 1, (0,) (see comment in link to "first 16 rows" by W. Lang) 2, 3, 4, 5,  6, 8,  9, 7,  10, 12, 15, 16, 18, 14, 20, 24, 27, 21, 25, 30, 32, 36, 11, 28, 40, 45, 48, 54, 35, 42, 50, 60, 64, 72, 81, 13, 22, 56, 63, 75, 80, 90, 96, 108, ... MATHEMATICA terms = 1000; nmax0 = 100000 (* a rough estimate of max sopfr *); sopfr[n_] := sopfr[n] = Total[Times @@@ FactorInteger[n]]; f[n1_, n2_] := Which[t1 = sopfr[n1]; t2 = sopfr[n2]; t1 < t2, True, t1 == t2, n1 <= n2, True, False]; Clear[g]; g[nmax_] := g[nmax] = Sort[Range[nmax], f][[1 ;; terms]]; g[nmax = nmax0]; g[nmax += nmax0]; While[g[nmax] != g[nmax - nmax0], Print[nmax]; nmax += nmax0]; A064364 = g[nmax] (* Jean-François Alcover, Mar 13 2019 *) PROG (Haskell) import Data.List (partition, union) a064364 n k = a064364_tabf !! (n-1) !! (k-1) a064364_row n = a064364_tabf !! (n-1) a064364_tabf =  : tail (f 1 [] 1 (map a000792 [2..])) where    f k pqs v (w:ws) = (map snd pqs') :      f (k + 1) (union pqs'' (zip (map a001414 us) us )) w ws where        us = [v + 1 .. w]        (pqs', pqs'') = partition ((== k) . fst) pqs a064364_list = concat a064364_tabf -- Reinhard Zumkeller, Jun 11 2015 CROSSREFS Cf. A001414. Cf. A000607 (row lengths), A002098 (row sums), A056240 (least = first term in the n-th row), A000792 (greatest term in the n-th row). Cf. A257815 (inverse). Sequence in context: A265568 A265552 A303936 * A303645 A332977 A269855 Adjacent sequences:  A064361 A064362 A064363 * A064365 A064366 A064367 KEYWORD easy,nonn,look,tabf AUTHOR Howard A. Landman, Sep 25 2001 EXTENSIONS More terms from Vladeta Jovovic, Sep 27 2005 STATUS approved

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Last modified July 16 13:35 EDT 2020. Contains 335788 sequences. (Running on oeis4.)