A258602 Smallest number m such that A069492(m) = prime(n)^5.

2, 5, 12, 20, 37, 45, 68, 82, 106, 142, 153, 194, 215, 227, 251, 290, 321, 336, 373, 395, 408, 442, 463, 499, 542, 566, 573, 600, 612, 634, 709, 728, 758, 769, 819, 831, 860, 895, 916, 947, 971, 980, 1034, 1043, 1057, 1069, 1131, 1190, 1208, 1219, 1240, 1265

Offset

1,1

Comments

A069492(a(n)) = A050997(n) = prime(n)^5;

A069492(m) mod prime(n) > 0 for m < a(n);

also smallest number m such that A258570(m) = prime(n):

A258570(a(n)) = A000040(n) and A258570(m) != A000040(n) for m < a(n).

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Example

.   n |  p |  a(n) | A069492(a(n)) = A050997(n) = p^5
. ----+----+-------+---------------------------------
.   1 |  2 |     2 |            32
.   2 |  3 |     5 |           243
.   3 |  5 |    12 |          3125
.   4 |  7 |    20 |         16807
.   5 | 11 |    37 |        161051
.   6 | 13 |    45 |        371293
.   7 | 17 |    68 |       1419857
.   8 | 19 |    82 |       2476099
.   9 | 23 |   106 |       6436343
.  10 | 29 |   142 |      20511149
.  11 | 31 |   153 |      28629151
.  12 | 37 |   194 |      69343957
.  13 | 41 |   215 |     115856201
.  14 | 43 |   227 |     147008443
.  15 | 47 |   251 |     229345007
.  16 | 53 |   290 |     418195493
.  17 | 59 |   321 |     714924299
.  18 | 61 |   336 |     844596301
.  19 | 67 |   373 |    1350125107
.  20 | 71 |   395 |    1804229351
.  21 | 73 |   408 |    2073071593
.  22 | 79 |   442 |    3077056399
.  23 | 83 |   463 |    3939040643
.  24 | 89 |   499 |    5584059449
.  25 | 97 |   542 |    8587340257  .

Prog

(Haskell)
import Data.List (elemIndex); import Data.Maybe (fromJust)
a258602 = (+ 1) . fromJust . (`elemIndex` a258570_list) . a000040

Crossrefs

Cf. a258570, A000040, A050997, A069492, A258599, A258600, A258601, A258603.

Sequence in context: A333558 A095306 A356649 * A327065 A307605 A079648

Adjacent sequences: A258599 A258600 A258601 * A258603 A258604 A258605

Keyword

nonn

Author

Reinhard Zumkeller, Jun 06 2015

Status

approved