A345950 - OEIS

%I #12 Jul 04 2021 22:05:48

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

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

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

%N a(n) = 1 if for all proper divisors d of n, A002034(d) < A002034(n), otherwise 0.

%H Antti Karttunen, <a href="/A345950/b345950.txt">Table of n, a(n) for n = 1..65537</a>

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

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>

%F a(n) = A010055(n) - [n is in A345946], where [ ] is the Iverson bracket.

%F For all n >= 1, A010051(n) <= a(n) <= A010055(n).

%o (PARI)

%o A002034(n) = if(1==n,n,my(s=factor(n)[, 1], k=s[#s], f=Mod(k!, n)); while(f, f*=k++); (k)); \\ After code in A002034.

%o A345950(n) = { my(x=A002034(n)); fordiv(n,d,if(A002034(d)==x,return(d==n))); };

%Y Characteristic function of A345944.

%Y Cf. A002034, A010051, A010055, A345945 (positions of zeros), A345946.

%Y Cf. also A344880.

%K nonn

%O 1

%A _Antti Karttunen_, Jul 04 2021