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A132982 The non-prime-power "antimutinous" numbers. (Antimutinous numbers are those integers m, m >1, where m/p^k < p, p = largest prime divisor of m, p^k = largest power of p that divides m.)

%I A132982 #13 Nov 19 2019 03:40:09
%S A132982 6,10,14,15,18,20,21,22,26,28,33,34,35,38,39,42,44,46,50,51,52,54,55,
%T A132982 57,58,62,65,66,68,69,74,75,76,77,78,82,85,86,87,88,91,92,93,94,95,98,
%U A132982 99,100,102,104,106,110,111,114,115,116,117,118,119,122,123,124,129,130
%N A132982 The non-prime-power "antimutinous" numbers. (Antimutinous numbers are those integers m, m >1, where m/p^k < p, p = largest prime divisor of m, p^k = largest power of p that divides m.)
%H A132982 Amiram Eldar, <a href="/A132982/b132982.txt">Table of n, a(n) for n = 1..10000</a>
%e A132982 30 = 2*3*5. 2*3 is > 5, so 30 is not in the sequence because 30 is mutinous (see A027854).
%e A132982 27 = 3^3. 27/3^3 is < 3, so 27 is antimutinous. But 27 is a power of a prime, so 27 is not in the sequence.
%e A132982 However, 20 = 2^2 * 5^1. And 20/5^1 is < 5, so 20 is antimutinous. Also, 20 is not a power of a prime. So 20 is in the sequence.
%t A132982 a = {}; For[n = 2, n < 200, n++, If[ !PrimeQ[n], If[ ! Length[FactorInteger[n]] == 1, b = FactorInteger[n]; m = 0; For[j = 1, j < Length[b] + 1, j++, If[b[[j, 1]]^b[[j, 2]] > m, m = b[[j, 1]]^b[[j, 2]]]; If[n/m < FactorInteger[m][[1, 1]], AppendTo[a, n]]]]]]; a (* _Stefan Steinerberger_, Nov 20 2007 *)
%Y A132982 Cf. A027854, A027855.
%K A132982 nonn
%O A132982 1,1
%A A132982 _Leroy Quet_, Nov 19 2007
%E A132982 More terms from _Stefan Steinerberger_, Nov 20 2007