A369977 - OEIS

%I #7 Feb 09 2024 15:49:07

%S 81,144,225,256,400,441,625,729,784,972,1089,1215,1225,1521,1620,1701,

%T 1728,1936,2160,2268,2401,2601,2673,2700,2704,2835,2880,3024,3025,

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

%C a(10) = 972 = 2^2 * 3^5 is the first term that is not a square.

%H Antti Karttunen, <a href="/A369977/b369977.txt">Table of n, a(n) for n = 1..20000</a>

%o (PARI)

%o A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };

%o A369001(n) = !(A083345(n)%2);

%o memoA369974 = Map();

%o 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 A369975(n) = (A369974(n)%2);

%o isA369977(n) = (A369001(n) && !A369975(n));

%Y Setwise difference A369002 \ A369976.

%Y Cf. A083345, A369001, A369974, A369975.

%K nonn

%O 1,1

%A _Antti Karttunen_, Feb 09 2024