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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)}.
0
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.
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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, May 04 2023
STATUS
approved