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 A067255 Irregular triangle read by rows: row n gives exponents in prime factorization of n. 35
 0, 1, 0, 1, 2, 0, 0, 1, 1, 1, 0, 0, 0, 1, 3, 0, 2, 1, 0, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 4, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 1, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 3, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Lengths of the runs are given by A061395(n),n>=2: [1,2,1,3,2,4,1,2,... ]. This sequence contains every finite sequence of nonnegative integers. - Franklin T. Adams-Watters, Jun 22 2005 LINKS Reinhard Zumkeller, Rows n = 1..250 of triangle, flattened Jeppe Stig Nielsen, See this explanation. EXAMPLE 1 = 2^0 2 = 2^1 3 = 2^0 3^1 4 = 2^2 5 = 2^0 3^0 5^1 6 = 2^1 3^1 ... and reading the exponents gives the sequence. Since for example 99=2^0*3^2*5^0*7^0*11^1, we use this symbol for ninety-nine: 99: {0,2,0,0,1}. Concatenating all the symbols for 1,2,3,4,5,6,..., we get the sequence. MATHEMATICA f[n_] := If[n == 1, {0}, Function[f, ReplacePart[Table[0, {PrimePi[f[[-1, 1]]]}], #] &@ Map[PrimePi@ First@ # -> Last@ # &, f]]@ FactorInteger@ n]; Array[f, 29] // Flatten (* Michael De Vlieger, Mar 08 2019 *) PROG (Haskell) a067255 n k = a067255_tabf !! (n-1) !! (k-1) a067255_row 1 = [0] a067255_row n = f n a000040_list where    f 1 _      = []    f u (p:ps) = g u 0 where      g v e = if m == 0 then g v' (e + 1) else e : f v ps              where (v', m) = divMod v p a067255_tabf = map a067255_row [1..] -- Reinhard Zumkeller, Jun 11 2013 CROSSREFS Cf. A133457. Cf. A001222, which gives the row sums of this table. For another version see A143078. Cf. A007814 (left edge), A071178 (right edge). Cf. A082786 (same as regular triangle). Cf. A054841, rows reversed and concatenated into a decimal number. Sequence in context: A029429 A064559 A336562 * A065716 A079409 A114643 Adjacent sequences:  A067252 A067253 A067254 * A067256 A067257 A067258 KEYWORD easy,nonn,tabf AUTHOR Jeppe Stig Nielsen, Feb 20 2002 STATUS approved

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Last modified September 29 12:15 EDT 2020. Contains 337431 sequences. (Running on oeis4.)