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 A120320 RF(5): refactorable numbers with smallest prime factor 5. 1
 625, 1500625, 9150625, 17850625, 37515625, 52200625, 73530625, 81450625, 174900625, 442050625, 577200625, 1171350625, 1766100625, 1838265625, 2136750625, 3049800625, 4931550625, 7573350625, 8653650625, 12594450625, 15882300625, 17748900625, 21970650625, 24343800625 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. All the terms are of the form 5^2 * A084967(k)^2 = 5^4 * A007310(k)^2. - Amiram Eldar, Aug 01 2024 LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 MAPLE 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; PROG (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 CROSSREFS Intersection of A033950 and A084967. Cf. A007310, A036896, A036897. Sequence in context: A187456 A223318 A222278 * A013837 A050448 A364073 Adjacent sequences: A120317 A120318 A120319 * A120321 A120322 A120323 KEYWORD nonn AUTHOR Walter Kehowski, Jun 20 2006 EXTENSIONS a(37)-a(40) from Amiram Eldar, Aug 01 2024 STATUS approved

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Last modified September 18 13:18 EDT 2024. Contains 376000 sequences. (Running on oeis4.)