A284763 Numbers n such that A279513(n) is squarefree.

1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 49, 51, 53, 55, 56, 57, 58, 59, 61, 62, 63, 65, 66, 67, 69, 70, 71, 73, 74, 75, 77, 78, 79, 82, 83, 85, 86, 87, 88, 89

Offset: 1

Author

Rémy Sigrist, Apr 02 2017

Keywords

• nonn

Comments

Also numbers with no duplicate prime number in their prime tower factorization (see A182318 for the definition of the prime tower factorization of a number).

This sequence contains the squarefree numbers (A005117); 8 = 2^3 is the first term in this sequence that is not squarefree.

All terms belong to A144146; 81 = 3^2^2 is the first term of A144146 that is not in this sequence.

Examples

			8 = 2^3 belongs to this sequence.
24 = 3*2^3 does not belong to this sequence.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A144146, A182318.

Programs

PARI

a279513(n) =  my (f=factor(n)); prod(i=1, #f~, f[i, 1]*a279513(f[i, 2]));
isok(n) = issquarefree(a279513(n)); \\ Michel Marcus, Apr 08 2017