A097320 error & a new related sequence

[David Wilson]

Yes it looks as if the author meant the exponents in the prime factorization 
strictly decrease, considering only the primes that divide the number in 
increasing order.

Thus 20 = 2^2 * 5^1 is in the sequence since we ignore the prime 3 which is 
not a divisor.  Otherwise, the exponents of 20 = 2^2 * 3^0 * 5^1 would not 
be strictly decreasing.

----- Original Message ----- 
From: "Leroy Quet" <qq-quet at mindspring.com>
To: <seqfan at ext.jussieu.fr>
Sent: Thursday, September 22, 2005 11:37 AM
Subject: A097320 error & a new related sequence


> In the example-line of sequence A097320 it says that 60 is in the
> sequence.
> But 60 is not among the terms given.
> Since 60 contains 2 primes which divide it only once each, then the error
> must be with the example line, since it seems that the author meant the
> the exponents are strickly decreasing when read from left to right in the
> prime factorizations of the terms of the sequence.
>
> Maybe someone could calculate and submit the related sequence where n is
> included if *at least one* exponent, when being read from left to right
> (raising the lowest prime to raising the highest prime) in the prime
> factorization of n, is less than the previous exponent.
> For example, 90 is included in this new sequence because 90 = 2^1 * 3^2 *
> 5^1, and the exponent 2 is greater than the exponent 1 raising the 5.
>
> thanks,
> Leroy Quet