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

1,2

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

Links

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Gus Wiseman, Sequences counting and encoding certain classes of multisets

Example

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

Mathematica

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

Prog

(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
(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

Crossrefs

See link for additional cross-references.

Cf. A000005, A000961, A001597, A007916, A303386, A327502.

Sequence in context: A243074 A304776 A052410 * A175781 A072775 A304768

Adjacent sequences: A327498 A327499 A327500 * A327502 A327503 A327504

Keyword

nonn

Author

Gus Wiseman, Sep 16 2019

Status

approved