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Composite "antimutinous" numbers. An antimutinous number is an integer m > 1 where m/p^k < p, where p is the largest prime divisor of m and p^k is the largest power of p dividing m.
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%I #14 Feb 24 2020 08:08:18

%S 4,6,8,9,10,14,15,16,18,20,21,22,25,26,27,28,32,33,34,35,38,39,42,44,

%T 46,49,50,51,52,54,55,57,58,62,64,65,66,68,69,74,75,76,77,78,81,82,85,

%U 86,87,88,91,92,93,94,95,98,99,100,102,104,106,110,111,114,115,116,117,118

%N Composite "antimutinous" numbers. An antimutinous number is an integer m > 1 where m/p^k < p, where p is the largest prime divisor of m and p^k is the largest power of p dividing m.

%C {a(k)-1} is the complement of sequence A056077. In other words, {a(k)} contains precisely those positive integers m where A001142(m-1) (= product{k=1 to m-1} k^(2k-m)) is not divisible by all primes <= m-1.

%H Amiram Eldar, <a href="/A132858/b132858.txt">Table of n, a(n) for n = 1..10000</a>

%t antiQ[n_] := Module[{f = FactorInteger[n], p, k}, p = f[[-1, 1]]; k = f[[-1, 2]]; n/p^k < p]; Select[Range[118], CompositeQ[#] && antiQ[#] &] (* _Amiram Eldar_, Feb 24 2020 *)

%Y Cf. A027855, A132982, A027854, A056077, A001142.

%K nonn

%O 1,1

%A _Leroy Quet_, Nov 21 2007

%E Extended by _Ray Chandler_, Nov 17 2008