A362814 Rectangular array read by descending antidiagonals; row n shows the numbers whose prime factorization p(1)^e(1)*p(2)^e(2)*... has n = max{e(k)}.

2, 3, 4, 5, 9, 8, 6, 12, 24, 16, 7, 18, 27, 48, 32, 10, 20, 40, 80, 96, 64, 11, 25, 54, 81, 160, 192, 128, 13, 28, 56, 112, 224, 320, 384, 256, 14, 36, 72, 144, 243, 448, 640, 768, 512, 15, 44, 88, 162, 288, 576, 896, 1280, 1536, 1024, 17, 45, 104, 176, 352

Offset

1,1

Comments

Every positive integer > 1 occurs exactly once.

Row n includes p^n for every prime p.

Row 1: the squarefree numbers >1, essentially A005117.

Links

Table of n, a(n) for n=1..60.

Example

Corner:
 2    3    5     6    7   10   11   13   14    15    17
 4    9   12    18   20   25   28   36   44    45    49
 8   24   27    40   54   56   72   88  104   108   120
16   48   80    81  112  144  162  176  208   240   272
32   96  160   224  243  288  352  416  480   486   544
64  192  320   448  576  704  729  832  960  1088  1216

Mathematica

t[n_] := t[n] = Max[Table[IntegerExponent[n, Prime[k]], {k, 1, n}]] ; (*A051903*)
s = Table[t[n], {n, 1, 5000}];
r[n_] := Take[Flatten[Position[s, n]], 15];
v = Table[r[n], {n, 1, 7}]
TableForm[v]

Crossrefs

Cf. A000040, A005117, A051903.

Sequence in context: A046021 A319023 A335910 * A371152 A266531 A284311

Adjacent sequences: A362811 A362812 A362813 * A362815 A362816 A362817

Keyword

nonn,tabl

Author

Clark Kimberling, May 04 2023

Status

approved