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, 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

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