A084296 Triangle: number of distinct prime factors in n-th primorial numbers when n prime factors first appears and in n-1 subsequent integers after.

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

Offset

1,2

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.

Links

Table of n, a(n) for n=1..103.

Example

n-th row of table consists of n numbers A001221[A002110(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.

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]

Crossrefs

Cf. A001221, A002110, A068069, A045983, A000217, A000124.

Sequence in context: A262891 A178340 A173261 * A209235 A062534 A143349

Adjacent sequences: A084293 A084294 A084295 * A084297 A084298 A084299

Keyword

nonn,tabl

Author

Labos Elemer, May 27 2003

Status

approved