[seqfan] Re: A123712 and A178212

Peter Luschny peter.luschny at googlemail.com
Thu Feb 9 20:14:20 CET 2012

CG> I have real interest in the underlying general question: what
CG> does a given sequence *mean*?

For me the meaning of a sequence is revealed in the shortest
arithmetical description of the sequence.

Under the assumption that A178212 = A123712 Reinhard found this
description with {n | Omega(n) > 3 and omega(n) = 3}.

CG> how do we understand a given sequence, when its definition
CG> requires a long chase through other sequences?

Presumably we do not understand this sequence yet. Or as Einstein
said: "You do not really understand something unless you can
explain it to your grandmother." I am happy to play the role of
the grandmother.

CG> Why do we care about the number of nonzero entries on a given row?
CG> What is the significance of the constant 16?

Paul seems to have found a much more general and interesting relation
with the matrix inverse of the triangle ([n/k]), n>=k>=1.

Thus I think the real question is: What is going on in A123706, or
what is the meaning of A123706(n,k) in arithmetical terms?


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