A139050 -id:A139050

Search: a139050 -id:a139050

Displaying 1-4 of 4 results found.

page 1

A139076

Let M(n) = maximal value of (n/k)^k over all k = 1, 2, ...; a(n) = floor(M(n)).

+10
5

1, 2, 3, 4, 6, 9, 12, 18, 27, 39, 57, 81, 118, 172, 244, 359, 517, 743, 1085, 1554, 2254, 3270, 4667, 6818, 9846, 14116, 20589, 29619, 42762, 62088, 89055, 129307, 187064, 267893, 390499, 563208, 811020, 1178088, 1694774, 2452059, 3551313, 5097655, 7405861, 10698505

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..44.

EXAMPLE

The sequence of M(n)'s begins 1, 2, 3, 4, 6.2500000000000000000, 9, 12.703703703703703703..., 18.962962962962962963..., 27, 39.062500000000000000, 57.191406250000000000, 81, 118.81376000000000000, 172.10368000000000000, 244.14062500000000000, ...

MAPLE

Digits:=20; g:=(n, k)->evalf( (n/k)^k );

# for M(n):

f:=proc(n) local i, a; global g; a:=1; for i from 1 to 2*n do if g(n, i) > a then a:=g(n, i); fi; od: a; end;

# for A139076:

f1:=proc(n) local i, a; global g; a:=1; for i from 1 to 2*n do if g(n, i) > a then a:=g(n, i); fi; od: floor(a); end;

# for A139077:

f2:=proc(n) local i, a; global g; a:=1; for i from 1 to 2*n do if g(n, i) > a then a:=g(n, i); fi; od: round(a); end;

# for A139078:

f3:=proc(n) local i, a; global g; a:=1; for i from 1 to 2*n do if g(n, i) > a then a:=g(n, i); fi; od: ceil(a); end;

CROSSREFS

Suggested by A000792. Cf. A139050, A139051, A139077, A139078.

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 03 2008

STATUS

approved

A139051

Denominator of fraction M(n) defined in A139076.

+10
4

1, 1, 1, 1, 4, 1, 27, 27, 1, 16, 256, 1, 3125, 3125, 64, 729, 46656, 823543, 823543, 823543, 16777216, 65536, 16777216, 19683, 387420489, 9765625, 10000000000, 9765625, 285311670611, 285311670611, 285311670611, 531441, 16777216, 302875106592253, 302875106592253

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

LINKS

Table of n, a(n) for n=1..35.

EXAMPLE

The sequence M(n), n >= 1, begins: 1, 2, 3, 4, 25/4, 9, 343/27, 512/27, 27, 625/16, 14641/256, 81, 371293/3125, 537824/3125, ...

CROSSREFS

Cf. A139050, A139076-A139078.

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Jun 03 2008

STATUS

approved

A139078

Let M(n) = maximal value of (n/k)^k over all k = 1, 2, ...; a(n) = ceiling(M(n)).

+10
4

1, 2, 3, 4, 7, 9, 13, 19, 27, 40, 58, 81, 119, 173, 245, 360, 518, 744, 1086, 1555, 2255, 3271, 4668, 6819, 9847, 14117, 20590, 29620, 42763, 62089, 89056, 129308, 187065, 267894, 390500, 563209, 811021, 1178089, 1694775, 2452060, 3551314, 5097656, 7405862, 10698506

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..44.

EXAMPLE

CROSSREFS

Suggested by A000792. Cf. A139050, A139051, A139076, A139077.

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 03 2008

STATUS

approved

A139077

Let M(n) = maximal value of (n/k)^k over all k = 1, 2, ...; a(n) = round(M(n)).

+10
2

1, 2, 3, 4, 6, 9, 13, 19, 27, 39, 57, 81, 119, 172, 244, 360, 517, 743, 1085, 1554, 2254, 3271, 4668, 6819, 9846, 14117, 20589, 29620, 42762, 62089, 89055, 129308, 187065, 267894, 390500, 563208, 811020, 1178088, 1694775, 2452059, 3551313, 5097655, 7405861, 10698505

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..44.

EXAMPLE

CROSSREFS

Suggested by A000792. Cf. A139050, A139051, A139076, A139078.

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 03 2008

STATUS

approved

page 1

Search completed in 0.067 seconds