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%I #14 Aug 01 2024 09:16:47
%S 625,1500625,9150625,17850625,37515625,52200625,73530625,81450625,
%T 174900625,442050625,577200625,1171350625,1766100625,1838265625,
%U 2136750625,3049800625,4931550625,7573350625,8653650625,12594450625,15882300625,17748900625,21970650625,24343800625
%N RF(5): refactorable numbers with smallest prime factor 5.
%C Numbers that are odd squares, 5 is their smallest prime factor, and are refactorable.
%C 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 5^(5-1) = 625 is the first element. Other elements would also be 5^4*17^4 or 5^16*17^4.
%C All the terms are of the form 5^2 * A084967(k)^2 = 5^4 * A007310(k)^2. - _Amiram Eldar_, Aug 01 2024
%H Amiram Eldar, <a href="/A120320/b120320.txt">Table of n, a(n) for n = 1..10000</a>
%p with(numtheory); RF5:=[]: p:=5: for w to 1 do for j from 1 to 12^5 do k:=2*j+1; if k mod 3 <> 0 and k mod p = 0 then n:=k^2; t:=tau(n); if (n mod t = 0) then RF5:=[op(RF5),n]; print(ifactor(n)); fi fi; od od;
%o (PARI) lista(kmax) = {my(m); for(k = 1, kmax, m = 25*(k\2*6-(-1)^k)^2; if(!(m % numdiv(m)), print1(m, ", ")));} \\ _Amiram Eldar_, Aug 01 2024
%Y Intersection of A033950 and A084967.
%Y Cf. A007310, A036896, A036897.
%K nonn
%O 1,1
%A _Walter Kehowski_, Jun 20 2006
%E a(37)-a(40) from _Amiram Eldar_, Aug 01 2024
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