A258776 -id:A258776 - cp's OEIS frontend

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

Robert Price, Jun 09 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. A258775 (indices of primes in this sequence), A258776 (corresponding primes).

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

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

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

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

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

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

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

A258775 Numbers n such that 1 + sigma(n)+ sigma(n)^2 is prime.

Original entry on oeis.org

1, 2, 5, 6, 7, 8, 11, 13, 14, 15, 19, 23, 34, 37, 40, 45, 49, 53, 57, 58, 60, 61, 78, 79, 89, 92, 105, 106, 109, 123, 129, 132, 137, 138, 140, 141, 143, 148, 149, 154, 155, 156, 160, 161, 163, 165, 167, 182, 188, 191, 193, 195, 201, 208, 212, 213, 222, 226

Offset: 1

Robert Price, Jun 09 2015

nonn

Also numbers n such that A000203(n) is in A002384. - Robert Israel, Jun 09 2015

Robert Price, Table of n, a(n) for n = 1..2122
OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Cf. A002384, A000203, A258774, A258776.

[n: n in [1..250] | IsPrime(1 + SumOfDivisors(n)+ SumOfDivisors(n)^2)]; // Vincenzo Librandi, Jun 10 2015

select(isprime @ (t -> 1+t+t^2) @ numtheory:-sigma, [$1..1000]); # Robert Israel, Jun 09 2015

Select[ Range[10000], PrimeQ[ 1 + DivisorSigma[1, #] + DivisorSigma[1, #]^2] & ]
Select[ Range[10000], PrimeQ[ Cyclotomic[3, DivisorSigma[1, #]]] &]

for(n=1,10^3,if(isprime(1+sigma(n)+sigma(n)^2),print1(n,", "))) \\ Derek Orr, Jun 09 2015

A259190 Primes of the form sigma(n) + sigma(n)^2 - 1.

Original entry on oeis.org

11, 19, 41, 71, 239, 181, 811, 599, 599, 991, 1559, 419, 599, 3659, 991, 3191, 929, 2351, 2969, 2351, 1481, 3659, 3191, 9311, 1979, 2351, 8741, 2969, 14519, 14519, 3659, 9311, 20879, 4691, 16001, 9311, 20879, 38219, 13109, 19739, 9311, 34781, 16001, 14519, 32579

Offset: 1

K. D. Bajpai, Jun 20 2015

nonn

These primes are not sorted nor unique. They are listed in the order found.

			a(2) = 19: sigma(3) + sigma(3)^2 - 1 = 4 + 16 - 1 = 19, which is prime.
a(5) = 239: sigma(8) + sigma(8)^2 - 1 = 15 + 225 - 1 = 239, which is prime.

K. D. Bajpai, Table of n, a(n) for n = 1..10000

Cf. A000040, A000203, A258776.

[k: n in [1..100] | IsPrime(k) where k is SumOfDivisors(n)+ SumOfDivisors(n)^2-1]; // K. D. Bajpai, Jun 20 2015

with(numtheory): A259190:= n-> (sigma(n) + sigma(n)^2-1): select(isprime,[seq((A259190 (n), n=1..500))]);

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

for(n=1, 100, k=sigma(n)+sigma (n)^2-1; if(isprime(k), print1(k,", "))); \\ K. D. Bajpai, Jun 20 2015

cp's OEIS Frontend

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

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A258775 Numbers n such that 1 + sigma(n)+ sigma(n)^2 is prime.

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Magma

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A259190 Primes of the form sigma(n) + sigma(n)^2 - 1.

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Crossrefs

Programs

Magma

Maple

Mathematica

PARI