A327502 a(n) = n/A327501(n), where A327501(n) is the maximum divisor of n that is 1 or not a perfect power.

1, 1, 1, 2, 1, 1, 1, 4, 3, 1, 1, 1, 1, 1, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 9, 1, 1, 1, 1, 16, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 32, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 1, 1, 1, 1, 1

Offset: 1

Author

Gus Wiseman, Sep 16 2019

Keywords

• nonn
• look

Comments

This maximum divisor is given by A327501.

A multiset is aperiodic if its multiplicities are relatively prime. The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). Heinz numbers of aperiodic multisets are numbers that are not perfect powers (A007916).

Examples

			The divisors of 36 that are 1 or not a perfect power are {1, 2, 3, 6, 12, 18}, so a(36) = 36/18 = 2.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16383
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Gus Wiseman, Sequences counting and encoding certain classes of multisets

Crossrefs

See link for additional cross-references.

Cf. A000005, A000961, A001597, A007916, A303386, A327501.

Programs

Mathematica

Table[n/Max[Select[Divisors[n],GCD@@Last/@FactorInteger[#]==1&]],{n,100}]

PARI

A327502(n) = if(n==1, 1, n/vecmax(select(x->((x>1) && !ispower(x)), divisors(n)))); \\ Antti Karttunen, Sep 19 2019 (after program given by Michel Marcus for A327501)

Formula

a(n) = n/A327501(n).