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A136575 A triangular sequence using Stan Wagon's LegendrePhi[a,b] function. 0
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, 11, 6, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 12, 6, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 13, 7, 5, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Row sums are: {0, 2, 4, 7, 9, 13, 15, 20, 22, 25, 27, 33, 35}.

LegendrePhi[n,a] gives the numbers of integers in [1, n] that are not divisible by any of the first a primes. - Ray Chandler, Oct 01 2015

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.

LINKS

Table of n, a(n) for n=1..105.

D. Bressoud, CNT.m Computational Number Theory Mathematica package.

FORMULA

t(n,m)=LegendrePhi[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]

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}

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]

CROSSREFS

Sequence in context: A164953 A136622 A025474 * A309898 A193592 A243714

Adjacent sequences:  A136572 A136573 A136574 * A136576 A136577 A136578

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Mar 26 2008

EXTENSIONS

Edited and extended by Ray Chandler, Oct 01 2015

STATUS

approved

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Last modified May 26 18:08 EDT 2020. Contains 334630 sequences. (Running on oeis4.)