|
|
A036303
|
|
Composite numbers whose prime factors contain no digits other than 1 and 3.
|
|
3
|
|
|
9, 27, 33, 39, 81, 93, 99, 117, 121, 143, 169, 243, 279, 297, 339, 341, 351, 363, 393, 403, 429, 507, 729, 837, 891, 933, 939, 961, 993, 1017, 1023, 1053, 1089, 1179, 1209, 1243, 1287, 1331, 1441, 1469, 1521, 1573, 1703, 1859, 2187, 2197, 2511, 2673, 2799
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
Sum_{n>=1} 1/a(n) = Product_{p in A020451} (p/(p - 1)) - Sum_{p in A020451} 1/p - 1 = 0.3374936085... . - Amiram Eldar, May 18 2022
|
|
EXAMPLE
|
The composite 117 = 3^2 * 13 is in the sequence as the digits of the prime factors are either 1 or 3. - David A. Corneth, Oct 17 2020
|
|
PROG
|
(Python)
from sympy import factorint
def ok(n):
f = factorint(n)
return sum(f.values()) > 1 and all(set(str(p)) <= set("13") for p in f)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|