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A175354 Numbers m such that reverse concatenations of divisors of m are nonprimes.

%I A175354 #15 Mar 21 2025 11:44:31
%S A175354 1,2,5,6,8,9,10,11,12,14,15,16,17,18,20,21,22,23,24,26,27,28,29,30,32,
%T A175354 33,34,35,36,37,38,40,41,42,44,45,46,47,49,50,51,52,53,54,55,56,57,58,
%U A175354 59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81
%N A175354 Numbers m such that reverse concatenations of divisors of m are nonprimes.
%C A175354 See A176558(n) = reverse concatenation of divisors of n. See A176588 for corresponding values of reverse concatenations. Complement of A089374(n) for n >= 2.
%H A175354 Harvey P. Dale, <a href="/A175354/b175354.txt">Table of n, a(n) for n = 1..1000</a>
%e A175354 Divisors of 12: 1, 2, 3, 4, 6, 12; reverse concatenation of divisors 1264321 is nonprime number.
%p A175354 filter:= proc(n) local r,L,i;
%p A175354   L:= sort(convert(numtheory:-divisors(n),list));
%p A175354   r:= L[1];
%p A175354   for i from 2 to nops(L) do
%p A175354    r:= r + 10^(1+ilog10(r))*L[i]
%p A175354   od;
%p A175354   not isprime(r)
%p A175354 end proc:
%p A175354 select(filter, [$1..100]); # _Robert Israel_, Apr 21 2020
%t A175354 Select[Range[90],!PrimeQ[FromDigits[Flatten[IntegerDigits/@Reverse[Divisors[#]]]]]&] (* _Harvey P. Dale_, Mar 21 2025 *)
%o A175354 (PARI) rcd(n)=my(d=divisors(n));n=1;for(i=2,#d,n=glue(d[i],n));n
%o A175354 glue(a,b)=a*10^#Str(b)+b
%o A175354 for(m=1,81,if(!isprime(rcd(m)),print1(m", ")))
%Y A175354 Cf. A089374, A176558, A176588.
%K A175354 nonn,base
%O A175354 1,2
%A A175354 _Jaroslav Krizek_, Apr 20 2010
%E A175354 Program, editing, and extension by _Charles R Greathouse IV_, Apr 23 2010
%E A175354 Corrected by _Jaroslav Krizek_, Apr 26 2010