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A372046 Composite numbers that divide the concatenation of the reverse of their ascending order prime factors, with repetition.

%I A372046 #23 May 10 2024 10:59:53
%S A372046 998,1636,9998,15584,49447,99998,1639964,2794612,9999998,15842836,
%T A372046 1639360636,1968390098,27879461212,65226742928
%N A372046 Composite numbers that divide the concatenation of the reverse of their ascending order prime factors, with repetition.
%C A372046 A number 999...9998 will be a term if it has two prime factors 2 and 4999...999. Therefore 999999999999998 and 999...9998 (with 54 9's) are both terms. See A056712.
%C A372046 100000000000 < a(15) <= 999999999999998.  _Robert P. P. McKone_, May 07 2024
%e A372046 998 is a term as 998 = 2 * 499 = "2" * "994" when each prime factor is reversed. This gives "2994", and 2994 is divisible by 998.
%e A372046 15584 is a term as 15584 = 2 * 2 * 2 * 2 * 2 * 487 = "2" * "2" * "2" * "2" * "2" * "784" when each prime factor is reversed. This gives "22222784", and 22222784 is divisible by 15584.
%t A372046 a[n_Integer] := Module[{f}, f = Flatten[ConstantArray @@@ FactorInteger[n]]; If[Length[f] < 2, Return[False]]; Mod[FromDigits[StringJoin[StringReverse[IntegerString[#, 10]] & /@ f], 10], n] == 0];
%t A372046 Select[Range[2, 10^5], a] (* _Robert P. P. McKone_, May 03 2024 *)
%o A372046 (Python)
%o A372046 from itertools import count, islice
%o A372046 from sympy import factorint
%o A372046 def A372046_gen(startvalue=4): # generator of terms >= startvalue
%o A372046     for n in count(max(startvalue,4)):
%o A372046         f = factorint(n)
%o A372046         if sum(f.values()) > 1:
%o A372046             c = 0
%o A372046             for p in sorted(f):
%o A372046                 a = pow(10,len(s:=str(p)),n)
%o A372046                 q = int(s[::-1])
%o A372046                 for _ in range(f[p]):
%o A372046                     c = (c*a+q)%n
%o A372046             if not c:
%o A372046                 yield n
%o A372046 A372046_list = list(islice(A372046_gen(),5)) # _Chai Wah Wu_, Apr 24 2024
%Y A372046 Cf. A371696, A371695, A371641, A027746, A056712.
%K A372046 nonn,base,more
%O A372046 1,1
%A A372046 _Scott R. Shannon_, Apr 17 2024
%E A372046 a(13)-a(14) from _Robert P. P. McKone_, May 05 2024