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A120320
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RF(5): refactorable numbers with smallest prime factor 5.
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1
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625, 1500625, 9150625, 17850625, 37515625, 52200625, 73530625, 81450625, 174900625, 442050625, 577200625, 1171350625, 1766100625, 1838265625, 2136750625, 3049800625, 4931550625, 7573350625, 8653650625, 12594450625, 15882300625, 17748900625, 21970650625, 24343800625
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OFFSET
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1,1
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COMMENTS
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Numbers that are odd squares, 5 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 5^(5-1) = 625 is the first element. Other elements would also be 5^4*17^4 or 5^16*17^4.
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LINKS
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MAPLE
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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;
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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