A139076 -id:A139076

A139050

Numerator of fraction M(n) defined in A139076.

+20
4

1, 2, 3, 4, 25, 9, 343, 512, 27, 625, 14641, 81, 371293, 537824, 15625, 262144, 24137569, 612220032, 893871739, 1280000000, 37822859361, 214358881, 78310985281, 134217728, 3814697265625, 137858491849, 205891132094649, 289254654976, 12200509765705829

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

OFFSET

1,2

LINKS

Table of n, a(n) for n=1..29.

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, ...

MAPLE

G:=(n, k)->(n/k)^k; 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;

CROSSREFS

Cf. A139051, A139076-A139078.

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Jun 03 2008

STATUS

approved

A139051

Denominator of fraction M(n) defined in A139076.

+20
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

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, ...

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

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, ...

CROSSREFS

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

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 03 2008

STATUS

approved