A285731 Transpose of square array A285730.

1, 2, 1, 3, 2, 1, 2, 3, 2, 1, 5, 4, 3, 2, 1, 3, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 2, 7, 6, 5, 4, 3, 2, 1, 3, 4, 7, 6, 5, 4, 3, 2, 1, 5, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 3, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 6, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 7, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

Offset: 1

Author

Antti Karttunen, Apr 28 2017

Keywords

• nonn
• tabl

Comments

See A285730.

Examples

			The top left 25 x 4 corner of the array:
  1 2 3 2 5 3 7 2 3  5 11  3 13  7  5  2 17  3 19  5  7 11 23  3  5
  1 2 3 4 5 6 7 4 9 10 11  6 13 14 15  4 17  9 19 10 21 22 23  6 25
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  8 17 18 19 20 21 22 23 12 25
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..7260; the first 120 antidiagonals of array

Crossrefs

Transpose of A285730.

Cf. A006530 (the topmost row).

Programs

Mathematica

With[{nn = 14}, Function[s, Table[s[[n, #]] &[k - n + 1], {k, nn}, {n, k, 1, -1}]]@ MapIndexed[PadRight[#1, nn, First@ #2] &, Table[FoldList[Times, Reverse@ Flatten[FactorInteger[n] /. {p_, e_} /; e > 0 :> ConstantArray[p, e]]], {n, nn}]]] // Flatten (* Michael De Vlieger, Apr 28 2017 *)

Python

from sympy import primefactors
def a006530(n): return 1 if n==1 else max(primefactors(n))
def A(n, k): return a006530(n) if k==1 else a006530(n)*A(n//a006530(n), k - 1)
for n in range(1, 21): print([A(n - k + 1, k) for k in range(1, n + 1)]) # Indranil Ghosh, Apr 28 2017

Scheme

(define (A285731 n) (A285730bi (A004736 n) (A002260 n))) ;; For A285730bi see A285730.