A327498 Maximum divisor of n whose prime multiplicities are distinct (A130091).

1, 2, 3, 4, 5, 3, 7, 8, 9, 5, 11, 12, 13, 7, 5, 16, 17, 18, 19, 20, 7, 11, 23, 24, 25, 13, 27, 28, 29, 5, 31, 32, 11, 17, 7, 18, 37, 19, 13, 40, 41, 7, 43, 44, 45, 23, 47, 48, 49, 50, 17, 52, 53, 54, 11, 56, 19, 29, 59, 20, 61, 31, 63, 64, 13, 11, 67, 68, 23

Offset: 1

Author

Gus Wiseman, Sep 16 2019

Keywords

• nonn
• easy

Comments

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

Every positive integer appears a finite number of times in the sequence; a prime p occurs 2^(PrimePi(p) - 1) times. - David A. Corneth, Sep 17 2019

Examples

			The divisors of 60 whose prime multiplicities are distinct are {1, 2, 3, 4, 5, 12, 20}, so a(60) = 20, the largest of these divisors.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000
• Gus Wiseman, Sequences counting and encoding certain classes of multisets

Crossrefs

See link for additional cross-references.

Cf. A000005, A000720, A007916, A098859, A124010, A181796, A212168, A255231, A327499, A351564.

Programs

Mathematica

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

PARI

a(n) = {my(m = Map(), f = factor(n), res = 1); forstep(i = #f~, 1, -1, forstep(j = f[i, 2], 1, -1, if(!mapisdefined(m, j), mapput(m, j, j); res*=f[i, 1]^j; next(2)))); res} \\ David A. Corneth, Sep 17 2019

PARI

A351564(n) = issquarefree(factorback(apply(e->prime(e),(factor(n)[,2]))));
A327498(n) = fordiv(n,d,if(A351564(n/d), return(n/d))); \\ Antti Karttunen, Apr 02 2022

Formula

a(A130091(n)) = n and a(A130092(n)) < n. - Ivan N. Ianakiev, Sep 17 2019

a(n) = n / A327499(n). - Antti Karttunen, Apr 02 2022