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 A120319 RF(3): refactorable numbers with smallest prime factor 3. 1
 9, 225, 441, 1089, 1521, 2025, 2601, 3249, 4761, 5625, 6561, 7569, 8649, 12321, 15129, 16641, 19881, 25281, 31329, 33489, 35721, 40401, 45369, 47961, 50625, 56169, 62001, 71289, 84681, 91809, 95481, 99225, 103041, 106929, 114921, 145161, 154449, 164025, 168921 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Numbers that are odd squares, 3 is their smallest prime factor, and are refactorable. 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. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 MAPLE 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; PROG (PARI) lista(kmax) = forstep(k = 3, kmax, 6, if(!(k^2 % numdiv(k^2)), print1(k^2, ", "))); \\ Amiram Eldar, Aug 01 2024 CROSSREFS Intersection of A016945 and A033950. Cf. A036896, A036897. Subsequence of A016946. Sequence in context: A033632 A110260 A036896 * A057530 A014736 A017558 Adjacent sequences: A120316 A120317 A120318 * A120320 A120321 A120322 KEYWORD nonn AUTHOR Walter Kehowski, Jun 20 2006 EXTENSIONS a(37)-a(39) from Amiram Eldar, Aug 01 2024 STATUS approved

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Last modified September 16 22:04 EDT 2024. Contains 375979 sequences. (Running on oeis4.)