A336868 Indicator function for numbers k such that k! has distinct prime multiplicities.

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, 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, 0, 0

Offset

0

Comments

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

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

Links

Table of n, a(n) for n=0..86.

Index entries for characteristic functions

Formula

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

Mathematica

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

Crossrefs

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

A336867 gives positions of zeros.

A130091 lists numbers with distinct prime multiplicities.

A181796 counts divisors with distinct prime multiplicities.

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

A336414 counts divisors of n! with distinct prime multiplicities.

A336415 counts divisors of n! with equal prime multiplicities.

A336866 counts partitions without distinct multiplicities.

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

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

Sequence in context: A082416 A093996 A323095 * A083187 A187036 A192490

Adjacent sequences: A336865 A336866 A336867 * A336869 A336870 A336871

Keyword

nonn

Author

Gus Wiseman, Aug 07 2020

Status

approved