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 A213925 Triangle read by rows: n-th row contains Fermi-Dirac representation of n. 39
 1, 2, 3, 4, 5, 2, 3, 7, 2, 4, 9, 2, 5, 11, 3, 4, 13, 2, 7, 3, 5, 16, 17, 2, 9, 19, 4, 5, 3, 7, 2, 11, 23, 2, 3, 4, 25, 2, 13, 3, 9, 4, 7, 29, 2, 3, 5, 31, 2, 16, 3, 11, 2, 17, 5, 7, 4, 9, 37, 2, 19, 3, 13, 2, 4, 5, 41, 2, 3, 7, 43, 4, 11, 5, 9, 2, 23, 47, 3, 16, 49, 2, 25 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Unique factorization of n into distinct prime powers of form p^(2^k), cf. A050376:  Product_{k=1..A064547(n)} T(n,k) = n. LINKS Alois P. Heinz, Rows n = 1..8000, flattened (first 1000 rows from Reinhard Zumkeller) OEIS Wiki, "Fermi-Dirac representation" of n EXAMPLE First rows: .     1:    1 .     2:    2 .     3:    3 .     4:    4 .     5:    5 .     6:    2  3 .     7:    7 .     8:    2  4                   8 = 2^2^0 * 2^2^1 .     9:    9 .    10:    2  5 ....... .   990:    2   5  9  11 .   991:  991 .   992:    2  16 31             992 = 2^2^0 * 2^2^2 * 31^2^0 .   993:    3 331 .   994:    2   7 71 .   995:    5 199 .   996:    3   4 83 .   997:  997 .   998:    2 499 .   999:    3   9 37             999 = 3^2^0 * 3^2^1 * 37^2^0 .  1000:    2   4  5  25        1000 = 2^2^0 * 2^2^1 * 5^2^0 * 5^2^1 . MAPLE T:= n-> `if`(n=1, [1], sort([seq((l-> seq(`if`(l[j]=1, i[1]^(2^(j-1)), [][]),              j=1..nops(l)))(convert(i[2], base, 2)), i=ifactors(n)[2])]))[]: seq(T(n), n=1..60);  # Alois P. Heinz, Feb 20 2018 MATHEMATICA nmax = 50; FDPrimes = Reap[k = 1; While[lim = nmax^(1/k); lim > 2, Sow[Prime[Range[PrimePi[lim]]]^k]; k = 2 k]][[2, 1]] // Flatten // Union; f[1] = 1; f[n_] := Reap[m = n; Do[If[m == 1, Break[], If[Divisible[m, p], m = m/p; Sow[p]]], {p, Reverse[FDPrimes]}]][[2, 1]] // Reverse; Array[f, nmax] // Flatten (* Jean-François Alcover, Feb 05 2019 *) PROG (Haskell) a213925 n k = a213925_row n !! (k-1) a213925_row 1 = [1] a213925_row n = reverse \$ fd n (reverse \$ takeWhile (<= n) a050376_list)    where fd 1 _      = []          fd x (q:qs) = if m == 0 then q : fd x' qs else fd x qs                        where (x', m) = divMod x q a213925_tabf = map a213925_row [1..] CROSSREFS Cf. A050376. For n > 1: A064547 (row lengths), A181894 (row sums), A223490, A223491. Sequence in context: A094937 A215089 A161768 * A141810 A141809 A309435 Adjacent sequences:  A213922 A213923 A213924 * A213926 A213927 A213928 KEYWORD nonn,tabf AUTHOR Reinhard Zumkeller, Mar 20 2013 EXTENSIONS Example corrected (row 992) by Reinhard Zumkeller, Mar 11 2015 STATUS approved

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Last modified October 18 15:41 EDT 2019. Contains 328162 sequences. (Running on oeis4.)