A113645 Numbers k such that sum of exponents in prime factorization of k (i.e., A001222(k)) is >= each prime divisor of k.

4, 8, 12, 16, 18, 24, 27, 32, 36, 48, 54, 64, 72, 80, 81, 96, 108, 120, 128, 144, 160, 162, 180, 192, 200, 216, 240, 243, 256, 270, 288, 300, 320, 324, 360, 384, 400, 405, 432, 448, 450, 480, 486, 500, 512, 540, 576, 600, 640, 648, 672, 675, 720, 729, 750, 768

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

A number k is included if A006530(k) <= A001222(k).

Example

12 = 2^2 *3^1. Since the sum of the prime factorization exponents, 2+1 = 3, is >= the largest prime dividing 12, which is 3, then 12 is included in the sequence.

Mathematica

fQ[n_] := Block[{f = FactorInteger@n}, Plus @@ Last /@ f >= Max[First /@ f]]; Select[ Range[2, 800], fQ@ # &] (* Robert G. Wilson v, Jan 16 2006 *)
qu[n_]:=n>1&&Block[{f=Transpose@FactorInteger@n, s}, s=Plus@@f[[2]]; s>=Max@f[[1]]]; L ={}; Do[If[qu[n], Print[n]; AppendTo[L, n]], {n, 1000}]; L (* Giovanni Resta, Jan 16 2006 *)

Prog

(PARI) isok(m) = {my(f=factor(m)); #select(x->(x>bigomega(f)), f[, 1]~) == 0; } \\ Michel Marcus, Sep 17 2020

Crossrefs

A proper subset of A068936.

Cf. A001222, A006530.

Sequence in context: A321177 A352490 A340788 * A311120 A311121 A351543

Adjacent sequences: A113642 A113643 A113644 * A113646 A113647 A113648

Keyword

nonn

Author

Leroy Quet, Jan 15 2006

Extensions

More terms from Robert G. Wilson v and Giovanni Resta, Jan 16 2006

Status

approved