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User:Charles R Greathouse IV

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Editor-in-Chief, interested primarily in computational number theory and allied fields.

I can be contacted via my Talk page here, or by email: my first name (charles) at my initials (crg4) dot com. Other email addresses may work as well.

User:Charles R Greathouse IV/Averages Early draft of an article.
User:Charles R Greathouse IV/Chase sequences 'Chase sequences': Axxxxxx refers to Ayyyyyy, which refers to Azzzzzz...
User:Charles R Greathouse IV/Favorites Some of my favorite sequences.
User:Charles R Greathouse IV/Format Discusses the correct format of b-files and how to repair ill-formatted b-files.
User:Charles R Greathouse IV/Junk Disreputable publishers, journals, etc.
User:Charles R Greathouse IV/Keywords Information on keywords: when to use them, new ones to add, etc.
User:Charles R Greathouse IV/Metadata Plans for OEIS metadata: keywords, categories, the index, etc.
User:Charles R Greathouse IV/Pari Some PARI/GP tools.
User:Charles R Greathouse IV/Programs Programs in the OEIS: types, format, etc.
User:Charles R Greathouse IV/Projects Other mathematical databases, fingerprint databases, and similar projects
User:Charles R Greathouse IV/Properties Sequence properties and classes
User:Charles R Greathouse IV/Rule of thumb Sequences should take 1 hour to prepare for submission.
User:Charles R Greathouse IV/Standards How to write up certain kinds of sequences.
User:Charles R Greathouse IV/Tables of special primes Types of primes and their densities
User:Charles R Greathouse IV/To do Sequences to work on and b-files to fix.
User:Charles R Greathouse IV/Vanity Sequences named after their discoverer.
User:Charles R Greathouse IV/Wiki Tools for the OEIS wiki.


Useful links:

Sequence of the Day

Sequence of the Day for October 20

A023194: Numbers
such that
σ (n)
is prime.
{ 2, 4, 9, 16, 25, 64, 289, 729, 1681, ... }

In 2005, Zak Seidov wondered why all terms except the first are squares.* Gabe Cunningham provided the answer:

“From the fact that (...) the sum-of-divisors function is multiplicative, we can derive that
σ (n)
is even except when
is a square or twice a square.”
n = 2 (2 k + 1) 2
, that is,
is twice an odd square, then
σ (n) = 3 σ ((2 k + 1) 2 )
. If
n = 2 (2 k ) 2
, that is,
is twice an even square, then
σ (n)
is only prime if
is a power of 2; otherwise we have
σ (n) = σ (8  ×  2m ) σ
for some positive integer
“So the only possible candidates for values of
other than squares such that
σ (n)
is prime are odd powers of 2. But
σ (2 2 m +1) = 2 2 m +2  −  1 = (2m +1 + 1) (2m +1  −  1)
, which is only prime when
m = 0
, that is, when
n = 2
. So 2 is the only nonsquare
such that
σ (n)
is prime.”


* A055638 Numbers
for which
σ (n 2 )
is prime:
{2, 3, 4, 5, 8, 17, 27, 41, 49, 59, 64, 71, 89, 101, 125, 131, 167, 169, 173, 256, 289, ...}

Sequences in the News

  • Dec 25 2018 German Heise-News "integers, please" column explains A003173 and OEIS.
  • Feb 01 2018 Alphabet announced a $8,589,869,056 = $A000396(6) stock buyback.
  • Jan 03 2018 Largest known term of A000043 announced: 77232917.
  • Nov 18 2016 PrimeGrid proves that 10223 is not a Sierpinski number, since 10223 × 2 31172165 + 1 is prime. So no changes to A076336 for now.
  • Sep 14 2016 Tom Greer discovers the twin primes 2996863034895 × 2 1290000 ± 1 using PrimeGrid, TwinGen and LLR.
  • Jan 19 2016 Largest known term of A000043 announced: 74207281, also discovered by Curtis Cooper.


I strive to live up to the highest ethical standards. If you feel that I have wrongly rejected one of your sequences (or otherwise failed to meet the expected standards), please leave a note at Complaints About Editing where it will be reviewed. I hope that in all cases you will first contact me (through the pink comment boxes, on my user page, or by email).