|
|
A072066
|
|
Exceptional (or extraordinary) numbers: m such that A005179(m) < A037019(m).
|
|
14
|
|
|
8, 16, 24, 32, 48, 64, 72, 80, 96, 108, 112, 128, 144, 160, 162, 176, 192, 208, 216, 224, 243, 256, 272, 288, 304, 320, 324, 352, 368, 384, 416, 432, 448, 464, 480, 486, 496, 512, 544, 576, 592, 608, 640, 648, 656, 672, 688, 704, 729, 736, 752, 768, 832, 848
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
The product of any exceptional numbers is an exceptional number. - Thomas Ordowski, Jun 14 2015
Grost proved that p^k is in the sequence if and only if 2^p < prime(k), where p is a prime. - Thomas Ordowski, Jun 15 2015
Only very few of the initial terms, {108, 162, 243, 324, 486, 729, ...} are not multiples of 8. Note that the 2nd to 6th in this list (and certainly more) equal 81*k = (10 + 1/8)*a(n) with n = 2, 3, 4, 5, 7, ... - M. F. Hasler, Jun 15 2022
|
|
LINKS
|
|
|
EXAMPLE
|
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|