A239133 Numbers n such that n^p_1 + n^p_2 + ... + n^p_k + 1 is prime where p_1,...p_k denote each prime factor of n, not necessarily distinct.

2, 8, 9, 12, 20, 28, 39, 48, 72, 90, 92, 96, 120, 128, 162, 272, 308, 340, 408, 472, 486, 510, 572, 690, 810, 912, 936, 972, 1107, 1224, 1312, 1444, 1632, 1734, 1870, 1890, 2002, 2106, 2432, 2592, 2912, 2916, 3004, 3068, 3768, 3834, 4256, 4394, 4557, 4725

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..112

Example

12 = 2*2*3 and 12^2+12^2+12^3+1 = 2017 is prime. Thus, 12 is a member of this sequence.

Maple

isA239133 := proc(n)
    ps := ifactors(n)[2] ;
    1+add( op(2, p)*n^op(1, p), p=ps) ;
    isprime(%) ;
end proc:
for n from 1 do
    if isA239133(n) then
        printf("%d, \n", n) ;
    end if;
end do: # R. J. Mathar, Mar 13 2014

Prog

(Python)
import sympy
from sympy import factorint
from sympy import isprime
def Exp(x):
..lst = []
..for i in range(len(factorint(x).values())):
....for a in range(list(factorint(x).values())[i]):
......lst.append(list(factorint(x))[i])
..num = 1
..for n in lst:
....num += x**n
..if isprime(num):
....return True
x = 1
while x < 10**4:
..if Exp(x):
....print(x)
..x += 1
(PARI) is(n)=my(f=factor(n)); ispseudoprime(sum(i=1, #f~, f[i, 2]*n^f[i, 1])+1) \\ Charles R Greathouse IV, Mar 12 2014

Crossrefs

Sequence in context: A120737 A081381 A235524 * A365517 A166686 A064833

Adjacent sequences: A239130 A239131 A239132 * A239134 A239135 A239136

Keyword

nonn

Author

Derek Orr, Mar 10 2014

Status

approved