A359543 - OEIS

%I #11 Jan 05 2023 18:30:57

%S 1,1,1,0,1,1,1,0,1,1,1,0,1,1,0,0,1,1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,1,

%T 0,0,1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,1,1,0,1,1,0,0,1,1,1,0,

%U 0,0,1,0,1,0,0,0,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,0,1,1,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,1,0,0,0,1,0,0,1

%N a(n) = 1 if A359542(n) = 0, otherwise a(n) = 0.

%C Question: What can be said about the distribution of 0's and 1's in this sequence? Compare also to A328308 and A359546.

%H Antti Karttunen, <a href="/A359543/b359543.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = [A359542(n) == 0], where [ ] is the Iverson bracket.

%F a(n) = [A359541(n) == A000005(n)].

%F a(n) <= A328308(n).

%o (PARI)

%o A003415checked(n) = if(n<=1, 0, my(f=factor(n), s=0); for(i=1, #f~, if(f[i, 2]>=f[i, 1], return(0), s += f[i, 2]/f[i, 1])); (n*s));

%o A341999(n) = if(!n,n,while(n>1, n = A003415checked(n)); (!n));

%o A359542(n) = sumdiv(n,d,A341999(d));

%o A359543(n) = (0==A359542(n));

%Y Characteristic function of A359544.

%Y Cf. A000005, A003415, A328308, A341999, A359541, A359542, A359546.

%K nonn

%O 1

%A _Antti Karttunen_, Jan 05 2023