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A136575
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A triangular sequence using Stan Wagon's LegendrePhi[a,b] function.
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0
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0, 1, 1, 2, 1, 1, 3, 2, 1, 1, 4, 2, 1, 1, 1, 5, 3, 2, 1, 1, 1, 6, 3, 2, 1, 1, 1, 1, 7, 4, 3, 2, 1, 1, 1, 1, 8, 4, 3, 2, 1, 1, 1, 1, 1, 9, 5, 3, 2, 1, 1, 1, 1, 1, 1, 10, 5, 3, 2, 1, 1, 1, 1, 1, 1, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Row sums are:
{0, 2, 4, 7, 9, 13, 15, 20, 22, 25, 27}
Wagon quote:
"Define the Legendre function a to be the number of positive integers m that are less than or equal to n and are not divisible by any of the first a primes a. "
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REFERENCES
| Bressoud & Wagon, A Course in Computational Number Theory, Springer/Key, 2000 (with a Mathematica package for computational number theory); http://www.msri.org/publications/ln/msri/2000/introant/wagon/mma/wagon_notes.nb.
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FORMULA
| t(n,m)=LengendrePhi[n,m] defined in Mathematica as: LegendrePhi[n_, 0] := n; LegendrePhi[n_, a_] := ((LegendrePhi[n, a] = LegendrePhi[n, a - 1] - LegendrePhi[Floor[n/Prime[a]], a - 1])
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EXAMPLE
| {0},
{1, 1},
{2, 1, 1},
{3, 2, 1, 1},
{4, 2, 1, 1, 1},
{5, 3, 2, 1, 1, 1},
{6, 3, 2, 1, 1, 1, 1},
{7, 4, 3, 2, 1, 1, 1, 1},
{8, 4, 3, 2, 1, 1, 1, 1, 1},
{9, 5, 3, 2, 1, 1, 1, 1, 1, 1},
{10, 5, 3, 2, 1, 1, 1, 1, 1, 1, 1}
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MATHEMATICA
| LegendrePhi[n_, 0] := n; LegendrePhi[n_, a_] := ((LegendrePhi[n, a] = LegendrePhi[n, a - 1] - LegendrePhi[Floor[n/Prime[a]], a - 1]); a = Table[Table[LegendrePhi[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[a]
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CROSSREFS
| Sequence in context: A164953 A136622 A025474 * A193592 A077592 A194005
Adjacent sequences: A136572 A136573 A136574 * A136576 A136577 A136578
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KEYWORD
| nonn,uned,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 26 2008
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