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A113645 Numbers k such that sum of exponents in prime factorization of k (i.e., A001222(k)) is >= each prime divisor of k. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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.
Sequence in context: A321177 A352490 A340788 * A311120 A311121 A351543
KEYWORD
nonn
AUTHOR
Leroy Quet, Jan 15 2006
EXTENSIONS
More terms from Robert G. Wilson v and Giovanni Resta, Jan 16 2006
STATUS
approved

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Last modified April 23 10:21 EDT 2024. Contains 371905 sequences. (Running on oeis4.)