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%I #26 Mar 13 2014 19:22:56
%S 2,8,9,12,20,28,39,48,72,90,92,96,120,128,162,272,308,340,408,472,486,
%T 510,572,690,810,912,936,972,1107,1224,1312,1444,1632,1734,1870,1890,
%U 2002,2106,2432,2592,2912,2916,3004,3068,3768,3834,4256,4394,4557,4725
%N 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.
%H Charles R Greathouse IV, <a href="/A239133/b239133.txt">Table of n, a(n) for n = 1..112</a>
%e 12 = 2*2*3 and 12^2+12^2+12^3+1 = 2017 is prime. Thus, 12 is a member of this sequence.
%p isA239133 := proc(n)
%p ps := ifactors(n)[2] ;
%p 1+add( op(2,p)*n^op(1,p),p=ps) ;
%p isprime(%) ;
%p end proc:
%p for n from 1 do
%p if isA239133(n) then
%p printf("%d,\n",n) ;
%p end if;
%p end do: # _R. J. Mathar_, Mar 13 2014
%o (Python)
%o import sympy
%o from sympy import factorint
%o from sympy import isprime
%o def Exp(x):
%o ..lst = []
%o ..for i in range(len(factorint(x).values())):
%o ....for a in range(list(factorint(x).values())[i]):
%o ......lst.append(list(factorint(x))[i])
%o ..num = 1
%o ..for n in lst:
%o ....num += x**n
%o ..if isprime(num):
%o ....return True
%o x = 1
%o while x < 10**4:
%o ..if Exp(x):
%o ....print(x)
%o ..x += 1
%o (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
%K nonn
%O 1,1
%A _Derek Orr_, Mar 10 2014
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