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User:Alonso del Arte

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Here is one of my projects: IMSLP Orchestra to do world premiere recording of Symphony by Franz Asplmayr.

I graduated from Wayne State University with a bachelor's degree in Film Studies in 2008. In 2004, I wrote for WSU's student newspaper, The South End, an article on the celebration for the 100,000th sequence to be added to the OEIS, A100000.

Sequence of the Day

Sequence of the Day for October 20

A023194: Numbers
n
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
n
is a square or twice a square.”
“If
n = 2 (2 k + 1) 2
, that is,
n
is twice an odd square, then
σ (n) = 3 σ ((2 k + 1) 2 )
. If
n = 2 (2 k) 2
, that is,
n
is twice an even square, then
σ (n)
is only prime if
n
is a power of 2; otherwise we have
σ (n) = σ (8  ×  2m ) σ
k
2m
for some positive integer
m
.”
“So the only possible candidates for values of
n
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
n
such that
σ (n)
is prime.”

_______________

* A055638 Numbers
n
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, ...}

Selected Recent Additions

  • A239797 Decimal expansion of .
  • A238271 Decimal expansion of .
  • A237042 UPC check digits.
  • A236603 Lowest canonical Gray cycles of length .
  • A235365 Smallest odd prime factor of .
  • A234522 Decimal expansion of .
  • A233748 Number of graphs on n vertices with edges colored with at most four interchangeable colors under the symmetries of the full edge permutation group.
  • A232499 Number of unit squares, aligned with a Cartesian grid, completely within the first quadrant of a circle centered at the origin ordered by increasing radius.
  • A231963 Concatenate with its UPC check digit.
  • A230624 Numbers with property that for every base , there is a number such that , where is the sum of digits in the base expansion of .


Sequences in the News

  • 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.
  • Mar 02 2014 Fredrik Johansson announces a computation of the partition number p(10 20) ≈ 1.8381765 × 10 11140086259, the largest known term of A000041.
  • Dec 06 2013 Microsoft launches a challenge to find large non-Mersenne primes, A138837.