A327499 Quotient of n over the maximum divisor of n whose prime multiplicities are distinct.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 3, 2, 5, 2, 1, 2, 3, 1, 1, 6, 1, 1, 1, 2, 1, 1, 1, 1, 3, 1, 1, 1, 5, 1, 3, 2, 1, 3, 1, 2, 1, 1, 5, 6, 1, 1, 3, 10, 1, 1, 1, 2, 1, 1, 7, 6, 1, 1, 1, 2, 1, 3, 5, 2, 3, 1, 1, 2, 7, 1, 3, 2, 5, 1, 1, 1, 1, 2, 1, 6, 1, 1, 15

Offset: 1

Author

Gus Wiseman, Sep 16 2019

Keywords

• nonn

Comments

A number's prime multiplicities are also called its (unsorted) prime signature.

Examples

			The maximum such divisor of 60 is 20, so a(60) = 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Gus Wiseman, Sequences counting and encoding certain classes of multisets

Crossrefs

See link for additional cross-references.

Cf. A000005, A098859, A124010, A130091, A255231, A327498, A327500, A351564.

Programs

Mathematica

Table[n/Max[Select[Divisors[n],UnsameQ@@Last/@FactorInteger[#]&]],{n,100}]

PARI

A351564(n) = issquarefree(factorback(apply(e->prime(e),(factor(n)[,2]))));
A327499(n) = fordiv(n,d,if(A351564(n/d), return(d))); \\ Antti Karttunen, Apr 02 2022

Formula

a(n) = n/A327498(n).

Extensions

Data section extended up to 105 terms by Antti Karttunen, Apr 02 2022