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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

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Last modified April 13 03:43 EDT 2021. Contains 342934 sequences. (Running on oeis4.)