A258774 a(n) = 1 + sigma(n) + sigma(n)^2.

3, 13, 21, 57, 43, 157, 73, 241, 183, 343, 157, 813, 211, 601, 601, 993, 343, 1561, 421, 1807, 1057, 1333, 601, 3661, 993, 1807, 1641, 3193, 931, 5257, 1057, 4033, 2353, 2971, 2353, 8373, 1483, 3661, 3193, 8191, 1807, 9313, 1981, 7141, 6163, 5257, 2353

Offset: 1

Author

Robert Price, Jun 09 2015

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A000203 (sum of divisors of n).

Cf. A258775 (indices of primes in this sequence), A258776 (corresponding primes).

Programs

Magma

[1+SumOfDivisors(n)+ SumOfDivisors(n)^2: n in [1..50]]; // Vincenzo Librandi, Jun 10 2015

Maple

with(numtheory): A258774:=n->1+sigma(n)+sigma(n)^2: seq(A258774(n), n=1..100); # Wesley Ivan Hurt, Jul 09 2015

Mathematica

Table[1 + DivisorSigma[1, n] + DivisorSigma[1, n]^2, {n, 10000}]
Table[Cyclotomic[3, DivisorSigma[1, n]], {n, 10000}]

PARI

a(n)=my(s=sigma(n)); s^2+s+1 \\ Charles R Greathouse IV, Jun 10 2015

Python

from sympy import divisor_sigma
def A258774(n):
    return (lambda x: x*(x+1)+1)(divisor_sigma(n)) # Chai Wah Wu, Jun 10 2015

Formula

a(n) = 1 + A000203(n) + A000203(n)^2.

a(n) = 1 + A000203(n) + A072861(n). - Omar E. Pol, Jun 19 2015