A258977 -id:A258977 - cp's OEIS frontend

A258974 a(n) = 1 + sigma(n)^2.

2, 10, 17, 50, 37, 145, 65, 226, 170, 325, 145, 785, 197, 577, 577, 962, 325, 1522, 401, 1765, 1025, 1297, 577, 3601, 962, 1765, 1601, 3137, 901, 5185, 1025, 3970, 2305, 2917, 2305, 8282, 1445, 3601, 3137, 8101, 1765, 9217, 1937, 7057, 6085, 5185, 2305

Offset: 1

Robert Price, Jun 15 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. A258976 (indices of primes in this sequence), A258977 (corresponding primes).

[(1 + DivisorSigma(1, n)^2): n in [1..50]]; // Vincenzo Librandi, Jun 16 2015

with(numtheory): A258974:=n->1+sigma(n)^2: seq(A258974(n), n=1..100); # Wesley Ivan Hurt, Jul 09 2015

Table[1 + DivisorSigma[1, n]^2, {n, 10000}]
Table[Cyclotomic[4, DivisorSigma[1, n]], {n, 10000}]

a(n)=sigma(n)^2+1 \\ Charles R Greathouse IV, Jun 18 2015

a(n) = 1 + A000203(n)^2.
a(n) = 1 + A072861(n). - Omar E. Pol, Jun 19 2015
a(n) = A002522(A000203(n)). - Michel Marcus, Jun 25 2015

A258976 Numbers n such that 1 + sigma(n)^2 is prime.

Original entry on oeis.org

1, 3, 5, 13, 14, 15, 19, 22, 23, 27, 28, 34, 39, 40, 44, 48, 53, 54, 56, 58, 65, 68, 73, 75, 82, 83, 84, 87, 88, 89, 95, 99, 104, 108, 109, 114, 116, 118, 124, 125, 129, 133, 134, 135, 136, 145, 149, 152, 158, 171, 177, 178, 179, 186, 202, 203, 209, 210, 215

Offset: 1

Robert Price, Jun 15 2015

nonn

Robert Price, Table of n, a(n) for n = 1..1786
OEIS Wiki, Cyclotomic Polynomials at x=n, n! and sigma(n)

Cf. A000203, A258974, A258977.

[n: n in [1..250] | IsPrime(1 + DivisorSigma(1, n)^2)]; // Vincenzo Librandi, Jun 16 2015

with(numtheory): A258976:=n->`if`(isprime(1+sigma(n)^2), n, NULL): seq(A258976(n), n=1..500); # Wesley Ivan Hurt, Jul 09 2015

Select[ Range[10000], PrimeQ[ 1 + DivisorSigma[1, #]^2] & ]
Select[ Range[10000], PrimeQ[ Cyclotomic[4, DivisorSigma[1, #]]] &]

lista(nn) = for (n=1, nn, if (isprime(1+sigma(n)^2), print1(n, ", "))); \\ Michel Marcus, Jun 17 2015

cp's OEIS Frontend

A258974 a(n) = 1 + sigma(n)^2.

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