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A120319 RF(3): refactorable numbers with smallest prime factor 3.

%I A120319 #12 Aug 01 2024 09:16:42
%S A120319 9,225,441,1089,1521,2025,2601,3249,4761,5625,6561,7569,8649,12321,
%T A120319 15129,16641,19881,25281,31329,33489,35721,40401,45369,47961,50625,
%U A120319 56169,62001,71289,84681,91809,95481,99225,103041,106929,114921,145161,154449,164025,168921
%N A120319 RF(3): refactorable numbers with smallest prime factor 3.
%C A120319 Numbers that are odd squares, 3 is their smallest prime factor, and are refactorable.
%C A120319 See A033950 for references. For any prime p, p^(p-1) is the smallest element of RF(p), the refactorable numbers whose smallest prime factor is p. Thus 3^(3-1)=9 is the first element. Other elements would also be 3^2*17^2 or 3^16*17^2.
%H A120319 Amiram Eldar, <a href="/A120319/b120319.txt">Table of n, a(n) for n = 1..10000</a>
%p A120319 with(numtheory); RF3:=[]: p:=3: for w to 1 do for j from 1 to 12^3 do k:=2*j+1; if k mod p = 0 then n:=k^2; t:=tau(n); if (n mod t = 0) then RF3:=[op(RF3),n]; print(ifactor(n)); fi fi; od od;
%o A120319 (PARI) lista(kmax) = forstep(k = 3, kmax, 6, if(!(k^2 % numdiv(k^2)), print1(k^2, ", "))); \\ _Amiram Eldar_, Aug 01 2024
%Y A120319 Intersection of A016945 and A033950.
%Y A120319 Cf. A036896, A036897.
%Y A120319 Subsequence of A016946.
%K A120319 nonn
%O A120319 1,1
%A A120319 _Walter Kehowski_, Jun 20 2006
%E A120319 a(37)-a(39) from _Amiram Eldar_, Aug 01 2024