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# User:Alonso del Arte

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 2 m
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 = (2 m +1 + 1) (2 m +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 ${\displaystyle {\frac {\sqrt {3}}{\sqrt[{3}]{4}}}}$.
• A238271 Decimal expansion of ${\displaystyle \sum _{n=1}^{\infty }{\frac {\mu (n)}{3^{n}}}}$.
• A237042 UPC check digits.
• A236603 Lowest canonical Gray cycles of length ${\displaystyle 2n}$.
• A235365 Smallest odd prime factor of ${\displaystyle 3^{n}+1}$.
• A234522 Decimal expansion of ${\displaystyle {\sqrt[{4}]{7}}-{\sqrt[{4}]{5}}}$.
• 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 ${\displaystyle n}$ with its UPC check digit.
• A230624 Numbers ${\displaystyle n}$ with property that for every base ${\displaystyle b\geq 2}$, there is a number ${\displaystyle m}$ such that ${\displaystyle m+s(m)=n}$, where ${\displaystyle s(m)}$ is the sum of digits in the base ${\displaystyle b}$ expansion of ${\displaystyle m}$.

## 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.