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%I #4 Jan 02 2019 23:14:39
%S 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,
%T 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,
%U 1,2,2,1,2,2,1,2,2,1,4,2,1,1,2,2,1,2,2
%N Irregular triangle read by rows where row n is the omega-sequence of n.
%C 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.
%C 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).
%e The sequence of omega-sequences begins:
%e 1: 26: 2 2 1 51: 2 2 1 76: 3 2 2 1
%e 2: 1 27: 3 1 52: 3 2 2 1 77: 2 2 1
%e 3: 1 28: 3 2 2 1 53: 1 78: 3 3 1
%e 4: 2 1 29: 1 54: 4 2 2 1 79: 1
%e 5: 1 30: 3 3 1 55: 2 2 1 80: 5 2 2 1
%e 6: 2 2 1 31: 1 56: 4 2 2 1 81: 4 1
%e 7: 1 32: 5 1 57: 2 2 1 82: 2 2 1
%e 8: 3 1 33: 2 2 1 58: 2 2 1 83: 1
%e 9: 2 1 34: 2 2 1 59: 1 84: 4 3 2 2 1
%e 10: 2 2 1 35: 2 2 1 60: 4 3 2 2 1 85: 2 2 1
%e 11: 1 36: 4 2 1 61: 1 86: 2 2 1
%e 12: 3 2 2 1 37: 1 62: 2 2 1 87: 2 2 1
%e 13: 1 38: 2 2 1 63: 3 2 2 1 88: 4 2 2 1
%e 14: 2 2 1 39: 2 2 1 64: 6 1 89: 1
%e 15: 2 2 1 40: 4 2 2 1 65: 2 2 1 90: 4 3 2 2 1
%e 16: 4 1 41: 1 66: 3 3 1 91: 2 2 1
%e 17: 1 42: 3 3 1 67: 1 92: 3 2 2 1
%e 18: 3 2 2 1 43: 1 68: 3 2 2 1 93: 2 2 1
%e 19: 1 44: 3 2 2 1 69: 2 2 1 94: 2 2 1
%e 20: 3 2 2 1 45: 3 2 2 1 70: 3 3 1 95: 2 2 1
%e 21: 2 2 1 46: 2 2 1 71: 1 96: 6 2 2 1
%e 22: 2 2 1 47: 1 72: 5 2 2 1 97: 1
%e 23: 1 48: 5 2 2 1 73: 1 98: 3 2 2 1
%e 24: 4 2 2 1 49: 2 1 74: 2 2 1 99: 3 2 2 1
%e 25: 2 1 50: 3 2 2 1 75: 3 2 2 1 100: 4 2 1
%t red[n_]:=Times@@Prime/@Last/@If[n==1,{},FactorInteger[n]];
%t omg[n_,k_]:=If[k==1,PrimeOmega[n],omg[red[n],k-1]];
%t dep[n_]:=If[n==1,0,If[PrimeQ[n],1,1+dep[Times@@Prime/@Last/@If[n==1,{},FactorInteger[n]]]]];
%t Table[omg[n,k],{n,100},{k,dep[n]}]
%Y Row lengths are A323014, or A182850 if we assume A182850(2) = 1.
%Y First column is empty if n = 1 and otherwise A001222(n).
%Y Second column is empty if n is 1 or prime and otherwise A001221(n).
%Y Third column is empty if n is 1, prime, or a power of a prime and otherwise A071625(n).
%Y Cf. A024619, A056239, A067340, A118914, A181819, A181821, A182857, A304464, A304465, A323022.
%K nonn,tabf
%O 1,3
%A _Gus Wiseman_, Jan 02 2019
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