

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 crossreferences.
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



