A259185 -id:A259185 - cp's OEIS frontend

A259184 a(n) = 1 - sigma(n) + sigma(n)^2.

1, 7, 13, 43, 31, 133, 57, 211, 157, 307, 133, 757, 183, 553, 553, 931, 307, 1483, 381, 1723, 993, 1261, 553, 3541, 931, 1723, 1561, 3081, 871, 5113, 993, 3907, 2257, 2863, 2257, 8191, 1407, 3541, 3081, 8011, 1723, 9121, 1893, 6973, 6007, 5113, 2257, 15253

Offset: 1

Robert Price, Jun 20 2015

Robert Price, Table of n, a(n) for n = 1..10000
OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Cf. A000203 (sum of divisors of n).

Cf. A259185 (indices of primes in this sequence), A259186 (corresponding primes).

with(numtheory): A259184:=n->1-sigma(n)+sigma(n)^2: seq(A259184(n), n=1..100); # Wesley Ivan Hurt, Jul 09 2015

Table[1 - DivisorSigma[1, n] + DivisorSigma[1, n]^2, {n, 10000}]
Table[Cyclotomic[6, DivisorSigma[1, n]], {n, 10000}]

a(n) = polcyclo(6, sigma(n)); \\ Michel Marcus, Jun 25 2015

a(n) = 1 - A000203(n) + A000203(n)^2.
a(n) = 1 - A000203(n) + A072861(n). - Omar E. Pol, Jun 20 2015
a(n) = A002061(A000203(n)). - Michel Marcus, Jun 25 2015

A259186 Primes in A259184.

Original entry on oeis.org

7, 13, 43, 31, 211, 157, 307, 757, 307, 1483, 1723, 3541, 1723, 5113, 3907, 8191, 3541, 8011, 1723, 6007, 5113, 5113, 14281, 5113, 14281, 8011, 3541, 28057, 20593, 20593, 5113, 37831, 28057, 17293, 14281, 8011, 12433, 28057, 20593, 14281, 24181, 10303, 46441

Offset: 1

Robert Price, Jun 20 2015

These primes are neither sorted nor uniqued. They are listed in the order found in A259184.

Robert Price, Table of n, a(n) for n = 1..1737
OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Cf. A000203, A259184, A259185.

with(numtheory): A259186:=n->`if`(isprime(1 - sigma(n) + sigma(n)^2), 1 - sigma(n) + sigma(n)^2, NULL): seq(A259186(n), n=1..200); # Wesley Ivan Hurt, Jul 09 2015

Select[Table[1 - DivisorSigma[1, n] + DivisorSigma[1, n]^2, {n, 10000}], PrimeQ]
Select[Table[Cyclotomic[6, DivisorSigma[1, n]], {n, 10000}], PrimeQ]

a(n) = A259184(A259185(n)).

cp's OEIS Frontend

A259184 a(n) = 1 - sigma(n) + sigma(n)^2.

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