A136575 A triangular sequence using Stan Wagon's LegendrePhi[a,b] function.

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

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