|
%I #33 May 18 2022 07:56:04
%S 9,27,33,39,81,93,99,117,121,143,169,243,279,297,339,341,351,363,393,
%T 403,429,507,729,837,891,933,939,961,993,1017,1023,1053,1089,1179,
%U 1209,1243,1287,1331,1441,1469,1521,1573,1703,1859,2187,2197,2511,2673,2799
%N Composite numbers whose prime factors contain no digits other than 1 and 3.
%C All terms are a product of at least two terms of A020451. - _David A. Corneth_, Oct 09 2020
%H David A. Corneth, <a href="/A036303/b036303.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Alois P. Heinz)
%H <a href="/index/Pri#prime_factors">Index entries for sequences related to prime factors</a>.
%F 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
%e 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
%o (Python)
%o from sympy import factorint
%o def ok(n):
%o f = factorint(n)
%o return sum(f.values()) > 1 and all(set(str(p)) <= set("13") for p in f)
%o print(list(filter(ok, range(2800)))) # _Michael S. Branicky_, Sep 27 2021
%Y Cf. A003597, A020451, A036302-A036325.
%K nonn,easy,base
%O 1,1
%A _Patrick De Geest_, Dec 15 1998
|
