[seqfan] Re: Meanings

franktaw at netscape.net franktaw at netscape.net
Tue Dec 13 15:17:44 CET 2011

There is no single answer to this question. The case you describe is 
especially problematic: both usages have been in the OEIS for a long 
time (relatively speaking). In fact, looking at the history, the usage 
in A024816 is actually the older one.  (The cited usage of 
multiply-anti-perfect is entirely consistent with the definition 
referenced in A073930, and is exactly analogous to the meaning of 
multiply perfect as compared to perfect - though it should probably be 
two separate words: multiply anti-perfect.)

Probably the best way forward for this case is that used, e.g., for 
"powerful numbers" (see A001694, A007532, A023052) - designate one as 
definition (1) and the other as the definition (2).

When an editor notices a new duplication of a definition in a 
submission, it will be suggested that some alternative be used. 
However, no systematic check for such duplication is made. Also, if the 
new definition comes from a published paper, it probably should be 

Franklin T. Adams-Watters

-----Original Message-----
From: Paolo Lava <paoloplava at gmail.com>

Dear seqfans,

What to do when the same word is used with different meanings? To take 
oldest definition as the right one or leave all the definitions as they 

For instance let us take the term “anti-perfect”.

I extensively used it in many sequences (see A192270, A192271, A192275,
A192285, A192288, A192290, A192293) trusting in the definition given by 
Perry: integers such that the sum of its anti-divisors equals the 
integers (A073930; the link does not work: see a cached copy on
anti-divisor in http://oeis.org/A066272/a066272a.html)

But if we look at A072228 Joseph L. Pe defines anti-perfect the numbers 
such that n = the sum of the reverses of the proper divisors of n.


Furthermore in a comment to A159907 Jaroslav Krizek writes: “…
multiply-anti-perfect numbers m: m divides antisigma(m) = A024816(m)…”



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