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A153446 Terms in A046034 which are pairwise products of terms in A046034.

%I A153446 #15 Aug 24 2022 09:53:05
%S A153446 25,35,75,225,275,375,525,575,2275,2325,2555,2775,3775,5575,5775,7575,
%T A153446 7725,7755,22575,22725,23275,23325,23725,25275,25375,25575,25725,
%U A153446 27335,27375,27775,32775,37275,37775,52325,53325,55225,55275,55575,57375
%N A153446 Terms in A046034 which are pairwise products of terms in A046034.
%C A153446 All terms are = 5 (mod 10).
%H A153446 David W. Wilson, <a href="/A153446/b153446.txt">Table of n, a(n) for n = 1..10410</a>
%e A153446 25 = 5*5 = A046034(3)*A046034(3) = A046034(7);
%e A153446 35 = 5*7 = A046034(3)*A046034(4) = A046034(11);
%e A153446 75 = 3*25 = A046034(2)*A046034(7) = A046034(19);
%e A153446 225 = 3*75 = A046034(2)*A046034(19) = A046034(23);
%e A153446 275 = 5*55 = A046034(3)*A046034(15) = A046034(35).
%t A153446 Select[Flatten@ Table[FromDigits /@ Tuples[{2, 3, 5, 7}, n], {n, 5}], Function[k, Total@ Map[Times @@ # &, Boole@ Map[Total@ Pick[DigitCount@ #, {1, 0, 0, 1, 0, 1, 0, 1, 1, 1}, 1] == 0 &, Transpose@ {#, k/#} &@ Rest@ Take[#, Ceiling[Length[#]/2]] &@ Divisors@ k, {2}]] > 0]] (* _Michael De Vlieger_, Sep 19 2016 *)
%t A153446 id[n_]:=IntegerDigits[n]; pQ[n_]:=AllTrue[id[n],PrimeQ];
%t A153446 nQ[n_]:=Select[Times@@@Tuples[Select[Divisors[n],AllTrue[id[#],PrimeQ]&],2],#==n&]
%t A153446 !={};
%t A153446 Select[Flatten@Table[FromDigits/@Tuples[{2,3,5,7},n],{n,5}],pQ[#]&&nQ[#]&] (* _Ivan N. Ianakiev_, Jul 20 2022 *)
%Y A153446 Cf. A046034 (numbers with prime digits).
%K A153446 base,nonn
%O A153446 1,1
%A A153446 _Zak Seidov_, Dec 26 2008