%I #18 Jul 01 2021 03:42:31

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

%T 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,

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

%N Indicator function for numbers k such that k! has distinct prime multiplicities.

%C Does this sequence contain only finitely many 1's (cf. A336867)?

%C A number has distinct prime multiplicities iff its prime signature is strict.

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

%F a(n) = 1 if n = 0, 1, 2, 4, 6, or 10 and a(n) = 0 otherwise (see A336867). - _Chai Wah Wu_, Aug 11 2020

%t Table[Boole[UnsameQ@@Last/@FactorInteger[n!]],{n,0,100}]

%Y A336499 has a(n) as the final term in row n.

%Y A336867 gives positions of zeros.

%Y A130091 lists numbers with distinct prime multiplicities.

%Y A181796 counts divisors with distinct prime multiplicities.

%Y A327498 gives the maximum divisor of n with distinct prime multiplicities.

%Y A336414 counts divisors of n! with distinct prime multiplicities.

%Y A336415 counts divisors of n! with equal prime multiplicities.

%Y A336866 counts partitions without distinct multiplicities.

%Y Cf. A098859, A118914, A124010, A336423, A336424, A336500, A336568, A336571.

%Y Factorial numbers: A000142, A007489, A022559, A027423, A048656, A048742, A071626, A325272, A325273, A325617, A336416.

%K nonn

%O 0

%A _Gus Wiseman_, Aug 07 2020