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

1,4

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).

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

Formula

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

Example

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.

Mathematica

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

Prog

(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)

Crossrefs

See link for additional cross-references.

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

Sequence in context: A140130 A337087 A321312 * A354090 A362826 A220632

Adjacent sequences: A327499 A327500 A327501 * A327503 A327504 A327505

Keyword

nonn,look

Author

Gus Wiseman, Sep 16 2019

Status

approved