|
| |
|
|
A259412
|
|
Primes of the form 1 - sigma(n) + sigma(n)^2 - sigma(n)^3 + sigma(n)^4.
|
|
3
|
|
|
|
61, 19141, 19141, 152381, 5200081, 5200081, 2031671, 5200081, 40454321, 250062751, 40454321, 212601841, 250062751, 1043960221, 1043960221, 310565641, 954091601, 1043960221, 619281791, 17315368621, 1043960221, 4278255361, 13640692231, 3415627931, 13640692231
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
These primes are neither sorted nor uniqued. They are listed in the order found in A259410.
|
|
|
LINKS
|
Robert Price, Table of n, a(n) for n = 1..1017
OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)
|
|
|
FORMULA
|
a(n) = A259410(A259411(n)).
|
|
|
MAPLE
|
with(numtheory): A259412:=n->`if`(isprime(1-sigma(n)+sigma(n)^2-sigma(n)^3+sigma(n)^4), 1-sigma(n)+sigma(n)^2-sigma(n)^3+sigma(n)^4, NULL): seq(A259412(n), n=1..500); # Wesley Ivan Hurt, Jun 27 2015
|
|
|
MATHEMATICA
|
Select[Table[1 - DivisorSigma[1, n] + DivisorSigma[1, n]^2 - DivisorSigma[1, n]^3 + DivisorSigma[1, n]^4, {n, 10000}], PrimeQ]
Select[Table[Cyclotomic[10, DivisorSigma[1, n]], {n, 10000}], PrimeQ]
Select[1-#+#^2-#^3+#^4&/@DivisorSigma[1, Range[300]], PrimeQ] (* Harvey P. Dale, Jul 07 2017 *)
|
|
|
PROG
|
(MAGMA) [a: n in [1..300] | IsPrime(a) where a is (1 - SumOfDivisors(n) + SumOfDivisors(n)^2 - SumOfDivisors(n)^3 + SumOfDivisors(n)^4)]; // Vincenzo Librandi, Jun 27 2015
|
|
|
CROSSREFS
|
Cf. A000203, A259410, A259411.
Sequence in context: A261238 A197105 A195216 * A099683 A337726 A057998
Adjacent sequences: A259409 A259410 A259411 * A259413 A259414 A259415
|
|
|
KEYWORD
|
easy,nonn
|
|
|
AUTHOR
|
Robert Price, Jun 26 2015
|
|
|
STATUS
|
approved
|
| |
|
|
