[seqfan] comments about perfect numbers

Maximilian Hasler maximilian.hasler at gmail.com
Tue Apr 21 23:36:56 CEST 2009

There are several comments about

A019279  Superperfect numbers
and to
A000396 Perfect numbers

and "formulae" for the latter,

a(n) = A000668(n)*(A000668(n)+1)/2. - Omar E. Pol
(info(AT)polprimos.com), Apr 23 2008
a(n) = A000217(A000668(n)). - Omar E. Pol (info(AT)polprimos.com), May 09 2008
a(n) = Sum of first A000668(n) positive integers. - Omar E. Pol
(info(AT)polprimos.com), May 09 2008
a(n) = A000384(A019279(n)) = A000384(A061652(n)). [From Omar E. Pol
(info(AT)polprimos.com), Aug 17 2008]
a(n) = A006516(A000043(n)). [From Omar E. Pol (info(AT)polprimos.com),
Aug 30 2008]
a(n) = A019279(n)*A000668(n) = A061652(n)*A000668(n). [From Omar E.
Pol (info(AT)polprimos.com), Jan 09 2009]

which seem to assume that A019279 is identical to A061652, and that no
odd perfect or superperfect numbers exist.

Unless one has a proof, one should not write the equalities (or
specify "conjectured" for the one among the two which is unproven),
and in comments one should specify which of the sequences is meant,
i.e. does the property follow from the fact that the number is
superperfect, or that it is 2^(p-1) where p is a Mersenne prime.

If a comment corresponds to a simple "experimental" observation, this
should also be specified
("it appears that...", "for all values known so far,..." etc),
according to the "IMPORTANT" note on
http://www.research.att.com/~njas/sequences/SubmitA.html .

Maximilian Hasler

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