

A327498


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


42



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
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OFFSET

1,2


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


LINKS

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


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


EXAMPLE

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.


MATHEMATICA

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


PROG

(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


CROSSREFS

See link for additional crossreferences.
Cf. A000005, A000720, A007916, A098859, A124010, A181796, A212168, A255231, A327499, A351564.
Sequence in context: A295126 A235602 A304180 * A111615 A348401 A324932
Adjacent sequences: A327495 A327496 A327497 * A327499 A327500 A327501


KEYWORD

nonn,easy


AUTHOR

Gus Wiseman, Sep 16 2019


STATUS

approved



