login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A327501 Maximum divisor of n that is 1 or not a perfect power. 3
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..69.

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 17 11:26 EDT 2021. Contains 343064 sequences. (Running on oeis4.)