A304038 Irregular triangle T(n,k) read by rows: first row is 0, n-th row (n > 1) lists indices of distinct primes dividing n.

0, 1, 2, 1, 3, 1, 2, 4, 1, 2, 1, 3, 5, 1, 2, 6, 1, 4, 2, 3, 1, 7, 1, 2, 8, 1, 3, 2, 4, 1, 5, 9, 1, 2, 3, 1, 6, 2, 1, 4, 10, 1, 2, 3, 11, 1, 2, 5, 1, 7, 3, 4, 1, 2, 12, 1, 8, 2, 6, 1, 3, 13, 1, 2, 4, 14, 1, 5, 2, 3, 1, 9, 15, 1, 2, 4, 1, 3, 2, 7, 1, 6, 16, 1, 2, 3, 5, 1, 4, 2, 8, 1, 10, 17, 1, 2, 3, 18, 1, 11

Offset: 1

Author

Ilya Gutkovskiy, May 05 2018

Keywords

• nonn
• tabf

Examples

			The irregular triangle begins:
1:  {0}
2:  {1}
3:  {2}
4:  {1}
5:  {3}
6:  {1, 2}
7:  {4}
8:  {1}
9:  {2}
10: {1, 3}
11: {5}
12: {1, 2}
		

Links

• Eric Weisstein's World of Mathematics, Distinct Prime Factors
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000040, A000720, A001221 (row lengths), A027748, A055396, A061395, A066328 (row sums), A112798, A156061 (row products), A302170.

Programs

Mathematica

Flatten[Table[PrimePi[FactorInteger[n][[All, 1]]], {n, 1, 62}]]

Formula

T(n,k) = A000720(A027748(n,k)).

T(n,1) = A055396(n).

T(n,A001221(n)) = A061395(n).