A036312 - OEIS

%I #28 May 18 2022 07:57:03

%S 4,8,14,16,28,32,49,56,64,98,112,128,196,224,256,343,392,448,454,512,

%T 554,686,784,896,908,1024,1108,1372,1454,1568,1589,1792,1816,1939,

%U 2048,2216,2401,2744,2908,3136,3178,3584,3632,3878,4096,4432,4802,5089,5488

%N Composite numbers whose prime factors contain no digits other than 2 and 7.

%C All terms are a product of at least two terms of A020459. - _David A. Corneth_, Oct 09 2020

%H David A. Corneth, <a href="/A036312/b036312.txt">Table of n, a(n) for n = 1..10000</a> (first 5340 terms from Robert Israel)

%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 A020459} (p/(p - 1)) - Sum_{p in A020459} 1/p - 1 = 0.7041098484... . - _Amiram Eldar_, May 18 2022

%p dmax:= 4: # for terms < 2*10^dmax

%p P:= {2,7}:

%p L:= {7}:

%p for d from 1 to dmax-1 do

%p   L:= map(t -> 2*10^d+t, L) union map(t -> 7*10^d+t, L);

%p   P:= P union select(isprime,L);

%p od:

%p R:= {1}: N:= 2*10^dmax:

%p for p in P do

%p   R:= R union map(t -> seq(t*p^j,j=1..floor(log[p](N/t))), R)

%p od:

%p sort(convert(R minus P minus {1},list)); # _Robert Israel_, Aug 04 2020

%Y Cf. A003591, A020459, A036302-A036325.

%K nonn,easy,base

%O 1,1

%A _Patrick De Geest_, Dec 15 1998