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A054522
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Triangle T(n,k): T(n,k) = phi(k) if k divides n, T(n,k)=0 otherwise (n >= 1, 1<=k<=n). T(n,k) = number of elements of order k in cyclic group of order n.
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20
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1, 1, 1, 1, 0, 2, 1, 1, 0, 2, 1, 0, 0, 0, 4, 1, 1, 2, 0, 0, 2, 1, 0, 0, 0, 0, 0, 6, 1, 1, 0, 2, 0, 0, 0, 4, 1, 0, 2, 0, 0, 0, 0, 0, 6, 1, 1, 0, 0, 4, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 1, 1, 2, 2, 0, 2, 0, 0, 0, 0, 0, 4, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 1, 1, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,6
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COMMENTS
| T(n,1) = 1; T(n,n) = A000010(n).
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LINKS
| Reinhard Zumkeller, Rows n=1..100 of triangle, flattened
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FORMULA
| Sum (T(n,k): k = 1 .. n) = n. [Reinhard Zumkeller, Oct 18 2011]
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EXAMPLE
| 1;
1, 1;
1, 0, 2;
1, 1, 0, 2;
1, 0, 0, 0, 4;
1, 1, 2, 0, 0, 2;
1, 0, 0, 0, 0, 0, 6;
1, 1, 0, 2, 0, 0, 0, 4;
1, 0, 2, 0, 0, 0, 0, 0, 6;
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MATHEMATICA
| t[n_, k_] /; Divisible[n, k] := EulerPhi[k]; t[_, _] = 0; Flatten[Table[t[n, k], {n, 1, 14}, {k, 1, n}]] (* From Jean-François Alcover, Nov 25 2011 *)
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PROG
| (PARI) T(n, k)=if(k<1|k>n, 0, if(n%k, 0, eulerphi(k)))
(Haskell)
a054522 n k = a054522_tabl !! (n-1) !! (k-1)
a054522_tabl = map a054522_row [1..]
a054522_row n = map (\k -> if n `mod` k == 0 then a000010 k else 0) [1..n]
-- Reinhard Zumkeller, Oct 18 2011
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CROSSREFS
| Cf. A054521.
Sequence in context: A166712 A035183 A178101 * A110250 A065252 A115211
Adjacent sequences: A054519 A054520 A054521 * A054523 A054524 A054525
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KEYWORD
| nonn,tabl,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Apr 09 2000
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