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

25, 35, 75, 225, 275, 375, 525, 575, 2275, 2325, 2555, 2775, 3775, 5575, 5775, 7575, 7725, 7755, 22575, 22725, 23275, 23325, 23725, 25275, 25375, 25575, 25725, 27335, 27375, 27775, 32775, 37275, 37775, 52325, 53325, 55225, 55275, 55575, 57375

Offset: 1

Author

Zak Seidov, Dec 26 2008

Keywords

• base
• nonn

Comments

All terms are = 5 (mod 10).

Examples

			25 = 5*5 = A046034(3)*A046034(3) = A046034(7);
35 = 5*7 = A046034(3)*A046034(4) = A046034(11);
75 = 3*25 = A046034(2)*A046034(7) = A046034(19);
225 = 3*75 = A046034(2)*A046034(19) = A046034(23);
275 = 5*55 = A046034(3)*A046034(15) = A046034(35).
		

Links

• David W. Wilson, Table of n, a(n) for n = 1..10410

Crossrefs

Cf. A046034 (numbers with prime digits).

Programs

Mathematica

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 *)
id[n_]:=IntegerDigits[n]; pQ[n_]:=AllTrue[id[n],PrimeQ];
nQ[n_]:=Select[Times@@@Tuples[Select[Divisors[n],AllTrue[id[#],PrimeQ]&],2],#==n&]
!={};
Select[Flatten@Table[FromDigits/@Tuples[{2,3,5,7},n],{n,5}],pQ[#]&&nQ[#]&] (* Ivan N. Ianakiev, Jul 20 2022 *)