A228122 Smallest nonnegative number x such that x^2 + x + 41 has exactly n prime factors counting multiplicities.

0, 40, 420, 1721, 14144, 139563, 3019035, 24304266, 206583092, 3838101265

Offset: 1

Author

Shyam Sunder Gupta, Aug 11 2013

Keywords

• nonn
• more

Examples

			a(1) = 0 because if x = 0 then x^2 + x + 41 = 41, which has 1 prime factor.
a(2) = 40 because if x = 40 then x^2 + x + 41 = 1681 = 41*41, which has 2 prime factors, counting multiplicities.
a(3) = 420 because if x = 420 then x^2 + x + 41 = 176861 = 47*53*71, which has 3 prime factors.
		

Crossrefs

Cf. A005846, A007634, A145292, A145293, A056561.

Programs

Mathematica

a = {}; Do[x = 0; While[PrimeOmega[x^2 + x + 41] != k, x++]; AppendTo[a, x], {k, 9}]; a

PARI

a(n) = {my(m=0); while (bigomega(m^2+m+41) != n, m++); m;} \\ Michel Marcus, Jan 31 2016

Python

from sympy import factorint
def A228122(n):
    k = 0
    while sum(factorint(k*(k+1)+41).values()) != n:
        k += 1
    return k # Chai Wah Wu, Sep 07 2018

Extensions

a(9) from Zak Seidov, Feb 01 2016

a(10) from Giovanni Resta, Sep 08 2018