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A127170
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Triangle read by rows: T(n,k) is the number of divisors of n that are divisible by k, with 1 <= k <= n.
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9
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1, 2, 1, 2, 0, 1, 3, 2, 0, 1, 2, 0, 0, 0, 1, 4, 2, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 4, 3, 0, 2, 0, 0, 0, 1, 3, 0, 2, 0, 0, 0, 0, 0, 1, 4, 2, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 4, 3, 2, 0, 2, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1
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OFFSET
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1,2
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COMMENTS
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Column k lists the terms of A000005 interleaved with k - 1 zeros.
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LINKS
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FORMULA
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T(n,k) = A000005(n/k), if k divides n, otherwise 0, with n >= 1 and 1 <= k <= n. - Omar E. Pol, Apr 01 2015
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EXAMPLE
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First 10 rows of the triangle:
1;
2, 1;
2, 0, 1;
3, 2, 0, 1;
2, 0, 0, 0, 1;
4, 2, 2, 0, 0, 1;
2, 0, 0, 0, 0, 0, 1;
4, 3, 0, 2, 0, 0, 0, 1;
3, 0, 2, 0, 0, 0, 0, 0, 1;
4, 2, 0, 0, 2, 0, 0, 0, 0, 1;
...
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MAPLE
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T:= (n, k)-> `if`(irem(n, k)=0, numtheory[tau](n/k), 0):
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MATHEMATICA
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Table[Function[D, Table[Count[D, _?(Mod[#, k] == 0 &)], {k, n}]]@ Divisors[n], {n, 12}] // Flatten (* Michael De Vlieger, Feb 16 2022 *)
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PROG
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(PARI) tabl(nn) = {m = matrix(nn, nn, n, k, if ((n % k) == 0, 1, 0)); m = m^2; for (n=1, nn, for (k=1, n, print1(m[n, k], ", "); ); print(); ); } \\ Michel Marcus, Apr 01 2015
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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8 terms taken from Example section and then corrected in Data section by Omar E. Pol, Mar 30 2015
New name (which was a comment dated Mar 30 2015) from Omar E. Pol, Feb 16 2022
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STATUS
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approved
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