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 A080688 Resort the index of A064553 using A080444 and maintaining ascending order within each grouping: seen as a triangle read by rows, the n-th row contains the A001055(n) numbers m with A064553(m)=n. 11
 1, 2, 3, 4, 5, 7, 6, 11, 13, 8, 10, 17, 9, 19, 14, 23, 29, 12, 15, 22, 31, 37, 26, 41, 21, 43, 16, 20, 25, 34, 47, 53, 18, 33, 38, 59, 61, 28, 35, 46, 67, 39, 71, 58, 73, 79, 24, 30, 44, 51, 55, 62, 83, 49, 89, 74, 97, 27, 57, 101, 52, 65, 82 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The number 12 can be written as 3*2*2, 4*3, 6*2 and 12 corresponding to each of the four values (12,15,22,31) in the example. Note that A001055(12) = 4. Since A001055(n) depends only on the least prime signature, the values 1,2,4,6,8,12,16,24,30,32,36,... A025487 are of special interest when counting multisets. (see for example, A035310 and a035341). A064553(T(n,k)) = A080444(n,k) = n for k=1..A001055(n); T(n,1) = A064554(n); T(n,A001055(n)) = A064554(n). - Reinhard Zumkeller, Oct 01 2012 Row n is the sorted list of shifted Heinz numbers of factorizations of n into factors > 1, where the shifted Heinz number of a factorization (y_1, ..., y_k) is prime(y_1 - 1) * ... * prime(y_k - 1). - Gus Wiseman, Sep 05 2018 LINKS Reinhard Zumkeller, Rows n = 1..1000 of triangle, flattened EXAMPLE a(18),a(19),a(20) and a(21) are 12,15,22 and 31 because A064553(12,15,22,31) = (12,12,12,12) similarly, A064553(36,45,66,76,93,95,118,121,149) = (36,36,36,36,36,36,36,36,36) From Gus Wiseman, Sep 05 2018: (Start) Triangle begins:    1    2    3    4  5    7    6 11   13    8 10 17    9 19   14 23   29   12 15 22 31   37   26 41   21 43   16 20 25 34 47 Corresponding triangle of factorizations begins:   (),   (2),   (3),   (2*2), (4),   (5),   (2*3), (6),   (7),   (2*2*2), (2*4), (8),   (3*3), (9),   (2*5), (10),   (11),   (2*2*3), (3*4), (2*6), (12). (End) MATHEMATICA facs[n_]:=If[n<=1, {{}}, Join@@Table[(Prepend[#1, d]&)/@Select[facs[n/d], Min@@#1>=d&], {d, Rest[Divisors[n]]}]]; Table[Sort[Table[Times@@Prime/@(f-1), {f, facs[n]}]], {n, 20}] (* Gus Wiseman, Sep 05 2018 *) PROG (Haskell) a080688 n k = a080688_row n !! (k-1) a080688_row n = map (+ 1) \$ take (a001055 n) \$                 elemIndices n \$ map fromInteger a064553_list a080688_tabl = map a080688_row [1..] a080688_list = concat a080688_tabl -- Reinhard Zumkeller, Oct 01 2012 CROSSREFS Cf. A001055, A025487, A035310, A035341, A064553, A080444. Cf. A007716, A056239, A162247, A215366, A275024, A317144, A317145, A318871. Sequence in context: A278505 A278506 A255546 * A082025 A076034 A336349 Adjacent sequences:  A080685 A080686 A080687 * A080689 A080690 A080691 KEYWORD easy,nonn,tabf AUTHOR Alford Arnold, Mar 23 2003 EXTENSIONS More terms from Sean A. Irvine, Oct 05 2011 Keyword tabf added and definition complemented accordingly by Reinhard Zumkeller, Oct 01 2012 STATUS approved

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Last modified September 21 09:06 EDT 2021. Contains 347597 sequences. (Running on oeis4.)