Riffs & Rotes

[Jon Awbrey]

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R&R.  Note 4

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Cf: http://www.research.att.com/projects/OEIS?Anum=A107532

Re: R&R 3.  http://stderr.org/pipermail/inquiry/2005-May/002718.html
In: R&R.    http://stderr.org/pipermail/inquiry/2005-May/thread.html#2714

Neil, SeqFans,

I have submitted this more general comment for A107532
that will update and obsolete my previous two comments.

The right diagonal labeled by the prime power of the form j:k = (prime(j))^k
contains the j^th power parts of positive integers raised to the k^th powers.
For example, the right diagonal labeled by the number 2 = 1:1 = (prime(1))^1
contains the power-free parts of each positive integer, specifically A055231,
and the right diagonal labeled by the number 4 = 1:2 = (prime(1))^2 contains
the squares of the square-free parts of positive integers.  In general, then,
the right diagonal labeled by m = (j_i : k_i)_i = Product_i prime(j_i)^(k_i)
contains the products over i of the (j_i)th power parts of positive integers
raised to the (k_i)th powers.

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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