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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
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
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.
Subsequence of A016946.
Sequence in context: A033632 A110260 A036896 * A057530 A014736 A017558
KEYWORD
nonn
AUTHOR
Walter Kehowski, Jun 20 2006
EXTENSIONS
a(37)-a(39) from Amiram Eldar, Aug 01 2024
STATUS
approved