cp's OEIS Frontend

A036319 Composite numbers whose prime factors have no digits other than 4's and 9's.

%I A036319 #35 May 22 2022 05:50:41
%S A036319 201601,224051,249001,2244551,2494501,4467101,4964551,19957601,
%T A036319 22180051,22225051,22449551,24700001,24949501,24990001,42632101,
%U A036319 42654551,47379551,47404501,49735051,90518849,98982601,100598899,111801449,124251499,199557601,221780051,222200551,247445501
%N A036319 Composite numbers whose prime factors have no digits other than 4's and 9's.
%C A036319 Closed under multiplication. - _David A. Corneth_, Sep 21 2020
%C A036319 From _M. F. Hasler_, Sep 22 2020: (Start)
%C A036319 Also closed under LCM, but not under GCD.
%C A036319 All terms are congruent to 1 or 9 (mod 10), depending on the parity of their number of prime factors counted with multiplicity, A001222. (End)
%H A036319 David A. Corneth, <a href="/A036319/b036319.txt">Table of n, a(n) for n = 1..10000</a>
%H A036319 <a href="/index/Pri#prime_factors">Index entries for sequences related to prime factors</a>.
%F A036319 Sum_{n>=1} 1/a(n) = Product_{p in A020466} (p/(p - 1)) - Sum_{p in A020466} 1/p - 1 = 0.00001523788893... . - _Amiram Eldar_, May 22 2022
%e A036319 The smallest prime made up of 4's and 9's is 449 (see A020466), so the smallest term here is 449^2 = 201601. - _N. J. A. Sloane_, Sep 21 2020
%t A036319 cn49Q[n_]:=Module[{fi=FactorInteger[n][[All,1]]},CompositeQ[n]&&Union[ Flatten[ IntegerDigits/@fi]]=={4,9}&&AllTrue[fi,PrimeQ]]; Select[Range[ 1,1006*10^5,2],cn49Q] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 21 2020 *)
%o A036319 (PARI) is(N)={!isprime(N)&& !#setminus(Set(concat(apply (digits, factor(N)[,1]))), [4,9])} \\ _M. F. Hasler_, Sep 22 2020
%Y A036319 Cf. A001222, A020466, A036302-A036325.
%K A036319 nonn,easy,base
%O A036319 1,1
%A A036319 _Patrick De Geest_, Dec 15 1998
%E A036319 More terms from _David A. Corneth_, Sep 21 2020