

A235524


Primitive refactorable (or tau) numbers: refactorable numbers which are not part of any family.


4



1, 2, 8, 9, 12, 18, 72, 80, 96, 108, 128, 288, 448, 625, 720, 864, 972, 1152, 1200, 1250, 1620, 1944, 2000, 2025, 2560, 4032, 4050, 5000, 5625, 6144, 6561, 6912, 7500, 7776, 9408, 10800, 11250, 11264, 12960, 13122, 16200, 18000, 18432, 19440, 20412, 21952
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

To be "primitive", the set of prime factors of N and of d(N) must be identical, otherwise any prime only in N is arbitrary and this defines a family of refactorable numbers. These are referred to as generators in the Zelinsky reference.
This sequence is therefore the intersection of the refactorable numbers (A033950) and those numbers with identical sets of prime factors for N and d(N) (A081381).
The first numbers in A081381 which are not in this sequence are 486, 768, 8748, and 303750. This sequence is A235525.


LINKS



EXAMPLE

720 is in the sequence since 720 = 2^4 * 3^2 * 5^1, therefore the prime decomposition of d(720) is 5 * 3 * 2 and each prime in 720 is required to make it refactorable.


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



