A302170 Irregular triangle T(n,k) read by rows: first row is 1, n-th row (n > 1) lists distinct prime factors of n in decreasing order.

1, 2, 3, 2, 5, 3, 2, 7, 2, 3, 5, 2, 11, 3, 2, 13, 7, 2, 5, 3, 2, 17, 3, 2, 19, 5, 2, 7, 3, 11, 2, 23, 3, 2, 5, 13, 2, 3, 7, 2, 29, 5, 3, 2, 31, 2, 11, 3, 17, 2, 7, 5, 3, 2, 37, 19, 2, 13, 3, 5, 2, 41, 7, 3, 2, 43, 11, 2, 5, 3, 23, 2, 47, 3, 2, 7, 5, 2, 17, 3, 13, 2, 53, 3, 2, 11, 5, 7, 2, 19, 3, 29, 2, 59, 5, 3, 2, 61, 31, 2

Offset: 1

Author

Ilya Gutkovskiy, Apr 02 2018

Keywords

• nonn
• tabf

Examples

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

Links

• Eric Weisstein's World of Mathematics, Distinct Prime Factors

Crossrefs

Cf. A001221 (row lengths), A006530, A008472 (row sums), A020639, A027746, A027748 (another version), A027750, A056538, A085307, A238689.

Programs

Haskell

a302170 n k = a302170_tabl !! (n-1) !! (k-1)
a302170_tabl = map a302170_row [1..]
a302170_row = reverse . a027748_row
-- Brian Chess, Sep 19 2022

Mathematica

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

Formula

T(n,1) = A006530(n).

T(n,A001221(n)) = A020639(n).