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A369977 Numbers that are found in A369002, but not in its subsequence A369976.

%I A369977 #7 Feb 09 2024 15:49:07
%S A369977 81,144,225,256,400,441,625,729,784,972,1089,1215,1225,1521,1620,1701,
%T A369977 1728,1936,2160,2268,2401,2601,2673,2700,2704,2835,2880,3024,3025,
%U A369977 3072,3159,3249,3375,3564,3600,3840,4032,4096,4131,4212,4225,4455,4500,4617,4624,4725,4752,4761,4800,5040,5120,5265,5292,5376
%N A369977 Numbers that are found in A369002, but not in its subsequence A369976.
%C A369977 a(10) = 972 = 2^2 * 3^5 is the first term that is not a square.
%H A369977 Antti Karttunen, <a href="/A369977/b369977.txt">Table of n, a(n) for n = 1..20000</a>
%o A369977 (PARI)
%o A369977 A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
%o A369977 A369001(n) = !(A083345(n)%2);
%o A369977 memoA369974 = Map();
%o A369977 A369974(n) = if(1==n,1,my(v); if(mapisdefined(memoA369974,n,&v), v, v = -sumdiv(n,d,if(d<n,A369001(n/d)*A369974(d),0)); mapput(memoA369974,n,v); (v)));
%o A369977 A369975(n) = (A369974(n)%2);
%o A369977 isA369977(n) = (A369001(n) && !A369975(n));
%Y A369977 Setwise difference A369002 \ A369976.
%Y A369977 Cf. A083345, A369001, A369974, A369975.
%K A369977 nonn
%O A369977 1,1
%A A369977 _Antti Karttunen_, Feb 09 2024