A327501 Maximum divisor of n that is 1 or not a perfect power.

1, 2, 3, 2, 5, 6, 7, 2, 3, 10, 11, 12, 13, 14, 15, 2, 17, 18, 19, 20, 21, 22, 23, 24, 5, 26, 3, 28, 29, 30, 31, 2, 33, 34, 35, 18, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 7, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 2, 65, 66, 67, 68, 69

Offset: 1

Author

Gus Wiseman, Sep 16 2019

Keywords

• nonn

Comments

First differs from A052410 at a(36) = 18, A052410(36) = 6.

The number of divisors that are 1 or not a perfect power is given by A327502.

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).

a(n) = n iff n is in A175082. - Bernard Schott, Sep 20 2019

Examples

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

Links

• Andrew Howroyd, 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, A000961, A001597, A007916, A303386, A327502.

Programs

Magma

[1] cat [Max([d:d in Divisors(n)| d gt 1 and not IsPower(d)]):n in [2..70]]; // Marius A. Burtea, Sep 20 2019

Mathematica

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

PARI

isp(n) = !ispower(n) && (n>1); \\ A007916
a(n) = if (n==1, 1, vecmax(select(x->isp(x), divisors(n)))); \\ Michel Marcus, Sep 18 2019