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

1,3

Links

Table of n, a(n) for n=1..100.

Eric Weisstein's World of Mathematics, Distinct Prime Factors

Index entries for sequences computed from indices in prime factorization

Formula

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

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

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

Example

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}

Mathematica

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

Crossrefs

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

Sequence in context: A341049 A144113 A370329 * A366113 A301983 A373889

Adjacent sequences: A304035 A304036 A304037 * A304039 A304040 A304041

Keyword

nonn,tabf

Author

Ilya Gutkovskiy, May 05 2018

Status

approved