A144146 -id:A144146 - cp's OEIS frontend

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

Rémy Sigrist, Apr 02 2017

nonn

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.

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

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

Cf. A005117, A144146, A182318.

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

A144147 A positive integer n is included if every exponent in the prime-factorization of n is coprime to n and if the sum of these prime-factorization exponents divides n.

Original entry on oeis.org

2, 3, 5, 6, 7, 10, 11, 13, 14, 17, 19, 22, 23, 26, 29, 30, 31, 34, 37, 38, 40, 41, 42, 43, 45, 46, 47, 53, 56, 58, 59, 61, 62, 63, 66, 67, 71, 73, 74, 75, 78, 79, 82, 83, 86, 88, 89, 94, 96, 97, 99, 101, 102, 103, 104, 105, 106, 107, 109, 113, 114, 117, 118, 122, 127, 131

Offset: 1

Leroy Quet, Sep 11 2008

nonn

All primes are included in the sequence. Any integer = 2*(odd prime) is included in the sequence. This sequence contains those terms in both sequence A074946 and sequence A144146.

			40 has the prime factorization of 2^3 * 5^1. The exponents are therefore 3 and 1. Both 3 and 1 are coprime to 40. And 3+1 = 4 divides 40. So 40 is included in the sequence.

A074946, A144146

Extended by Ray Chandler, Nov 04 2008

cp's OEIS Frontend

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

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