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A286563
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Triangular table T(n,k) read by rows: T(n,1) = 1, and for 1 < k <= n, T(n,k) = the highest exponent e such that k^e divides n.
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8
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1, 1, 1, 1, 0, 1, 1, 2, 0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 3, 0, 1, 0, 0, 0, 1, 1, 0, 2, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
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OFFSET
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1,8
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COMMENTS
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LINKS
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FORMULA
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T(n,k) = A286561(n,k) listed row by row for n >= 1, k = 1 .. n.
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EXAMPLE
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The first fifteen rows of this triangular table:
1,
1, 1,
1, 0, 1,
1, 2, 0, 1,
1, 0, 0, 0, 1,
1, 1, 1, 0, 0, 1,
1, 0, 0, 0, 0, 0, 1,
1, 3, 0, 1, 0, 0, 0, 1,
1, 0, 2, 0, 0, 0, 0, 0, 1,
1, 1, 0, 0, 1, 0, 0, 0, 0, 1,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
1, 2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1,
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1,
1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1,
1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
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MATHEMATICA
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Table[If[k == 1, 1, IntegerExponent[n, k]], {n, 15}, {k, n}] // Flatten (* Michael De Vlieger, May 20 2017 *)
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PROG
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(Python)
def T(n, k):
i=1
if k==1: return 1
while n%(k**i)==0:
i+=1
return i-1
for n in range(1, 21): print([T(n, k) for k in range(1, n + 1)]) # Indranil Ghosh, May 20 2017
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CROSSREFS
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Lower triangular region of A286561.
Cf. A286564 (same triangle reversed).
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KEYWORD
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AUTHOR
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STATUS
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approved
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