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

1,2

Links

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

Eric Weisstein's World of Mathematics, Distinct Prime Factors

Formula

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

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

Example

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}

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A112764 A108728 A331962 * A049805 A104887 A064886

Adjacent sequences: A302167 A302168 A302169 * A302171 A302172 A302173

Keyword

nonn,tabf

Author

Ilya Gutkovskiy, Apr 02 2018

Status

approved