cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A036303 Composite numbers whose prime factors contain no digits other than 1 and 3.

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%I A036303 #35 Jan 08 2025 18:32:35
%S A036303 9,27,33,39,81,93,99,117,121,143,169,243,279,297,339,341,351,363,393,
%T A036303 403,429,507,729,837,891,933,939,961,993,1017,1023,1053,1089,1179,
%U A036303 1209,1243,1287,1331,1441,1469,1521,1573,1703,1859,2187,2197,2511,2673,2799
%N A036303 Composite numbers whose prime factors contain no digits other than 1 and 3.
%C A036303 All terms are a product of at least two terms of A020451. - _David A. Corneth_, Oct 09 2020
%H A036303 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 A036303 <a href="/index/Pri#prime_factors">Index entries for sequences related to prime factors</a>.
%F A036303 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 A036303 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
%t A036303 Select[Range[3000],CompositeQ[#]&&SubsetQ[{1,3},Union[Flatten[IntegerDigits/@FactorInteger[#][[;;,1]]]]]&] (* _Harvey P. Dale_, Jan 08 2025 *)
%o A036303 (Python)
%o A036303 from sympy import factorint
%o A036303 def ok(n):
%o A036303     f = factorint(n)
%o A036303     return sum(f.values()) > 1 and all(set(str(p)) <= set("13") for p in f)
%o A036303 print(list(filter(ok, range(2800)))) # _Michael S. Branicky_, Sep 27 2021
%Y A036303 Cf. A003597, A020451, A036302-A036325.
%K A036303 nonn,easy,base
%O A036303 1,1
%A A036303 _Patrick De Geest_, Dec 15 1998