A120319 RF(3): refactorable numbers with smallest prime factor 3.

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

Offset

1,1

Comments

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

Table of n, a(n) for n=1..36.

Formula

a(n) = odd square, 3 is the smallest prime factor and refactorable.

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;

Crossrefs

Cf. A033950, A036896, A036897.

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

Status

approved