cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A285731 Transpose of square array A285730.

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%I A285731 #17 Jun 12 2025 12:56:52
%S A285731 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,
%T A285731 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,
%U A285731 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
%N A285731 Transpose of square array A285730.
%C A285731 See A285730.
%H A285731 Antti Karttunen, <a href="/A285731/b285731.txt">Table of n, a(n) for n = 1..7260; the first 120 antidiagonals of array</a>
%e A285731 The top left 25 x 4 corner of the array:
%e A285731   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
%e A285731   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
%e A285731   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
%e A285731   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
%t A285731 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 *)
%o A285731 (Scheme) (define (A285731 n) (A285730bi (A004736 n) (A002260 n))) ;; For A285730bi see A285730.
%o A285731 (Python)
%o A285731 from sympy import primefactors
%o A285731 def a006530(n): return 1 if n==1 else max(primefactors(n))
%o A285731 def A(n, k): return a006530(n) if k==1 else a006530(n)*A(n//a006530(n), k - 1)
%o A285731 for n in range(1, 21): print([A(n - k + 1, k) for k in range(1, n + 1)]) # _Indranil Ghosh_, Apr 28 2017
%Y A285731 Transpose of A285730.
%Y A285731 Cf. A006530 (the topmost row).
%K A285731 nonn,tabl
%O A285731 1,2
%A A285731 _Antti Karttunen_, Apr 28 2017