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A084296
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Triangle: number of distinct prime factors in n-th primorial numbers when n prime factors first appears and in n-1 subsequent integers after.
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0
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1, 2, 1, 3, 1, 1, 4, 1, 2, 2, 5, 1, 2, 2, 3, 6, 2, 2, 3, 2, 2, 7, 3, 2, 3, 3, 2, 4, 8, 2, 3, 2, 4, 2, 3, 2, 9, 2, 3, 3, 3, 2, 4, 3, 4, 10, 3, 3, 2, 2, 2, 4, 3, 3, 2, 11, 1, 4, 3, 2, 4, 5, 4, 3, 3, 4, 12, 3, 3, 4, 2, 3, 6, 2, 3, 5, 4, 3, 13, 3, 4, 2, 3, 3, 3, 3, 3, 3, 6, 2, 4, 14, 2, 3, 2, 4, 5, 4, 5, 3, 3, 6, 4
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Omega-values(=A001221) in the subsequent neighborhood of radius n, for primorial numbers are usually neither all distinct or all equal items as it is required in A068069, A045983 sequences.
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EXAMPLE
| n-th row of table consists of n numbers A001221[A02110(n+j)], j=0...n-1:
1,
2,1,
3,1,1,
4,1,2,2,
5,1,2,2,3,
6,2,2,3,2,2,
7,3,2,3,3,2,4,
Rows starts with n at indices which are central polygonal numbers:a[A000124(n)]=n; rows ends at a[A000217(n)] terms, at triangular number indices.
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MATHEMATICA
| lf[x_] := Length[FactorInteger[x]] q[x_] := Apply[Times, Table[Prime[w], {w, 1, x}]] Flatten[Table[Table[lf[q[n]+j], {j, 0, n-1}], {n, 1, 20}], 1]
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CROSSREFS
| Cf. A001221, A002110, A068069, A045983, A000217, A000124.
Sequence in context: A113924 A178340 A173261 * A062534 A143349 A182715
Adjacent sequences: A084293 A084294 A084295 * A084297 A084298 A084299
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KEYWORD
| nonn,tabl
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), May 27 2003
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