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 A323023 Irregular triangle read by rows where row n is the omega-sequence of n. 52
 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 1, 2, 1, 2, 2, 1, 1, 3, 2, 2, 1, 1, 2, 2, 1, 2, 2, 1, 4, 1, 1, 3, 2, 2, 1, 1, 3, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 4, 2, 2, 1, 2, 1, 2, 2, 1, 3, 1, 3, 2, 2, 1, 1, 3, 3, 1, 1, 5, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 4, 2, 1, 1, 2, 2, 1, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS We define the omega-sequence of n to have length A323014(n), and the k-th term is Omega(red^{k-1}(n)), where Omega = A001222 and red^{k} is the k-th functional iteration of A181819. Except for n = 1, all rows end with 1. If n is not prime, the term in row n prior to the last is A304465(n). LINKS EXAMPLE The sequence of omega-sequences begins:    1:            26: 2 2 1      51: 2 2 1        76: 3 2 2 1    2: 1          27: 3 1        52: 3 2 2 1      77: 2 2 1    3: 1          28: 3 2 2 1    53: 1            78: 3 3 1    4: 2 1        29: 1          54: 4 2 2 1      79: 1    5: 1          30: 3 3 1      55: 2 2 1        80: 5 2 2 1    6: 2 2 1      31: 1          56: 4 2 2 1      81: 4 1    7: 1          32: 5 1        57: 2 2 1        82: 2 2 1    8: 3 1        33: 2 2 1      58: 2 2 1        83: 1    9: 2 1        34: 2 2 1      59: 1            84: 4 3 2 2 1   10: 2 2 1      35: 2 2 1      60: 4 3 2 2 1    85: 2 2 1   11: 1          36: 4 2 1      61: 1            86: 2 2 1   12: 3 2 2 1    37: 1          62: 2 2 1        87: 2 2 1   13: 1          38: 2 2 1      63: 3 2 2 1      88: 4 2 2 1   14: 2 2 1      39: 2 2 1      64: 6 1          89: 1   15: 2 2 1      40: 4 2 2 1    65: 2 2 1        90: 4 3 2 2 1   16: 4 1        41: 1          66: 3 3 1        91: 2 2 1   17: 1          42: 3 3 1      67: 1            92: 3 2 2 1   18: 3 2 2 1    43: 1          68: 3 2 2 1      93: 2 2 1   19: 1          44: 3 2 2 1    69: 2 2 1        94: 2 2 1   20: 3 2 2 1    45: 3 2 2 1    70: 3 3 1        95: 2 2 1   21: 2 2 1      46: 2 2 1      71: 1            96: 6 2 2 1   22: 2 2 1      47: 1          72: 5 2 2 1      97: 1   23: 1          48: 5 2 2 1    73: 1            98: 3 2 2 1   24: 4 2 2 1    49: 2 1        74: 2 2 1        99: 3 2 2 1   25: 2 1        50: 3 2 2 1    75: 3 2 2 1     100: 4 2 1 MATHEMATICA red[n_]:=Times@@Prime/@Last/@If[n==1, {}, FactorInteger[n]]; omg[n_, k_]:=If[k==1, PrimeOmega[n], omg[red[n], k-1]]; dep[n_]:=If[n==1, 0, If[PrimeQ[n], 1, 1+dep[Times@@Prime/@Last/@If[n==1, {}, FactorInteger[n]]]]]; Table[omg[n, k], {n, 100}, {k, dep[n]}] CROSSREFS Row lengths are A323014, or A182850 if we assume A182850(2) = 1. First column is empty if n = 1 and otherwise A001222(n). Second column is empty if n is 1 or prime and otherwise A001221(n). Third column is empty if n is 1, prime, or a power of a prime and otherwise A071625(n). Cf. A024619, A056239, A067340, A118914, A181819, A181821, A182857, A304464, A304465, A323022. Sequence in context: A141591 A174545 A102523 * A083415 A115514 A326038 Adjacent sequences:  A323020 A323021 A323022 * A323024 A323025 A323026 KEYWORD nonn,tabf AUTHOR Gus Wiseman, Jan 02 2019 STATUS approved

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Last modified August 18 01:04 EDT 2019. Contains 326059 sequences. (Running on oeis4.)