%I
%S 1,1,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,
%T 0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,
%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1
%N a(n) = 1 if n is a highly composite number (A002182), 0 otherwise.
%C Characteristic function of A002182, first differences of A261100, MÃ¶bius transform of A181801.
%H Antti Karttunen, <a href="/A322586/b322586.txt">Table of n, a(n) for n = 1..83160</a>
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(1) = 1; for n > 1, a(n) = A261100(n)  A261100(n1).
%F For all n, a(n) <= A322585(n).
%o (PARI)
%o v002182 = vector(128); v002182[1] = 1; \\ For memoization.
%o A002182(n) = { my(d,k); if(v002182[n],v002182[n], k = A002182(n1); d = numdiv(k); while(numdiv(k) <= d, k=k+1); v002182[n] = k; k); };
%o A261100(n) = { my(k=1); while(A002182(k)<=n,k=k+1); (k1); };
%o A322586(n) = if(1==n,1,(A261100(n)A261100(n1)));
%Y Cf. A002182, A181801, A261100 (partial sums), A322585.
%K nonn
%O 1
%A _Antti Karttunen_, Dec 20 2018
