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

1,2

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 cross-references.

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

Sequence in context: A295126 A235602 A304180 * A111615 A358668 A348401

Adjacent sequences: A327495 A327496 A327497 * A327499 A327500 A327501

Keyword

nonn,easy

Author

Gus Wiseman, Sep 16 2019

Status

approved