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A027751
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Irregular triangle read by rows in which row n lists the proper divisors of n (those divisors of n which are < n), with the first row {1} by convention.
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45
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1, 1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 2, 4, 1, 3, 1, 2, 5, 1, 1, 2, 3, 4, 6, 1, 1, 2, 7, 1, 3, 5, 1, 2, 4, 8, 1, 1, 2, 3, 6, 9, 1, 1, 2, 4, 5, 10, 1, 3, 7, 1, 2, 11, 1, 1, 2, 3, 4, 6, 8, 12, 1, 5, 1, 2, 13, 1, 3, 9, 1, 2, 4, 7, 14, 1, 1, 2, 3, 5, 6, 10, 15, 1, 1, 2, 4, 8, 16, 1, 3, 11, 1, 2, 17, 1, 5, 7, 1, 2, 3, 4, 6, 9, 12, 18
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refs;
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history;
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internal format)
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OFFSET
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1,5
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COMMENTS
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Or, take the list 1,2,3,4,... of natural numbers (A000027) and replace each number by its proper divisors.
The row length is 1 for n = 1 and A032741(n) for n >= 2. - Wolfdieter Lang, Jan 16 2016
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LINKS
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Alois P. Heinz, Rows n = 1..1540, flattened
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EXAMPLE
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The irregular triangle T(n,k) begins:
n\k 1 2 3 4 5 ...
1: 1 (by convention)
2: 1
3: 1
4: 1 2
5: 1
6: 1 2 3
7: 1
8: 1 2 4
9: 1 3
10: 1 2 5
11: 1
12: 1 2 3 4 6
13: 1
14: 1 2 7
15: 1 3 5
16: 1 2 4 8
17: 1
18: 1 2 3 6 9
19: 1
20: 1 2 4 5 10
.... reformatted - Wolfdieter Lang, Jan 16 2016
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MAPLE
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with(numtheory):
T:= n-> sort([(divisors(n) minus {n})[]])[]: T(1):=1:
seq(T(n), n=1..50); # Alois P. Heinz, Apr 11 2012
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MATHEMATICA
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Table[ Divisors[n] // Most, {n, 1, 36}] // Flatten // Prepend[#, 1] & (* Jean-François Alcover, Jun 10 2013 *)
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PROG
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(Haskell)
a027751 n k = a027751_tabf !! (n-1) !! (k-1)
a027751_row n = a027751_tabf !! (n-1)
a027751_tabf = [1] : map init (tail a027750_tabf)
-- Reinhard Zumkeller, Apr 18 2012
(Python)
from sympy import divisors
def a(n): return [1] if n==1 else divisors(n)[:-1]
for n in range(21): print(a(n)) # Indranil Ghosh, Apr 30 2017
(PARI) row(n) = if (n==1, [1], my(d = divisors(n)); vector(#d-1, k, d[k])); \\ Michel Marcus, Apr 30 2017
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CROSSREFS
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Cf. A027750, A032741 (row lengths), A001065, A000005.
Row sums give A173455. - Omar E. Pol, Nov 23 2010
Sequence in context: A228107 A140207 A104763 * A181322 A004070 A180562
Adjacent sequences: A027748 A027749 A027750 * A027752 A027753 A027754
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KEYWORD
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nonn,easy,tabf
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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More terms from Patrick De Geest, May 15 1998
Example edited by Omar E. Pol, Nov 23 2010
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STATUS
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approved
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