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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 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[]; s>=Max@f[]]; 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

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Last modified May 27 02:41 EDT 2022. Contains 354093 sequences. (Running on oeis4.)