cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A248775 Greatest 7th-power-free divisor of n!.

Original entry on oeis.org

1, 2, 6, 24, 120, 720, 5040, 315, 2835, 28350, 311850, 3742200, 48648600, 681080400, 10216206000, 1277025750, 21709437750, 178678500, 3394891500, 67897830000, 1425854430000, 31368797460000, 721482341580000, 135277939046250, 3381948476156250
Offset: 1

Views

Author

Clark Kimberling, Oct 14 2014

Keywords

Examples

			a(8) = 315 because 315 divides 8! and if k > 315 divides 8!, then h^7 divides 8!/k for some h > 1.

Links

Crossrefs

Cf. A248773, A248774, A000142.

Programs

  • Mathematica
    z = 50; f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
m = 7; Table[p[m, n], {n, 1, z}]  (* A248773 *)
Table[p[m, n]^(1/m), {n, 1, z}]   (* A248774 *)
Table[n!/p[m, n], {n, 1, z}]      (* A248775 *)

Formula

a(n) = n!/A248773(n).

A248778 Greatest 8th-power-free divisor of n!.

Original entry on oeis.org

1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 14175, 155925, 1871100, 24324300, 340540200, 5108103000, 81729648000, 1389404016000, 14889875, 282907625, 5658152500, 118821202500, 2614066455000, 60123528465000, 1442964683160000, 36074117079000000
Offset: 1

Views

Author

Clark Kimberling, Oct 14 2014

Keywords

Examples

			a(8) = 315 because 315 divides 8! and if k > 315 divides 8!, then h^7 divides 8!/k for some h > 1.

Links

Crossrefs

Cf. A248776, A248777, A000142.

Programs

  • Mathematica
    z = 60; f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
m = 8; Table[p[m, n], {n, 1, z}]  (* A248776 *)
Table[p[m, n]^(1/m), {n, 1, z}]   (* A248777 *)
Table[n!/p[m, n], {n, 1, z}]      (* A248778 *)

Formula

a(n) = n!/A248773(n).

A248774 Greatest k such that k^7 divides n!

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 4, 4, 12, 12, 12, 12, 12, 12, 24, 24, 24, 24, 24, 24, 360, 360, 720, 720, 720, 720, 720, 720, 1440, 1440, 1440, 1440, 1440, 1440, 1440, 4320, 8640, 8640, 8640, 60480, 60480, 60480, 120960, 120960, 120960, 120960
Offset: 1

Views

Author

Clark Kimberling, Oct 14 2014

Keywords

Comments

Every term divides all its successors.

Examples

			a(8) = 2 because 2^7 divides 8! and if k > 2 then k^7 does not divide 8!.

Links

Crossrefs

Cf. A248774, A248775, A000142.

Programs

  • Mathematica
    z = 50; f[n_] := f[n] = FactorInteger[n!]; r[m_, x_] := r[m, x] = m*Floor[x/m];
u[n_] := Table[f[n][[i, 1]], {i, 1, Length[f[n]]}];
v[n_] := Table[f[n][[i, 2]], {i, 1, Length[f[n]]}];
p[m_, n_] := p[m, n] = Product[u[n][[i]]^r[m, v[n]][[i]], {i, 1, Length[f[n]]}];
m = 7; Table[p[m, n], {n, 1, z}]  (* A248773 *)
Table[p[m, n]^(1/m), {n, 1, z}]   (* A248774 *)
Table[n!/p[m, n], {n, 1, z}]      (* A248775 *)
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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