A180852 Numbers n such that the sum_i (d_i^i) of the i-th powers of their sorted divisors d_1< d_2<...< n is prime.

2, 9, 18, 5618, 7744, 10000, 28561, 30258, 34322, 40000, 46225, 165649, 200978, 249218, 258064, 310472, 370881, 393129, 425042, 438244, 542882, 595984, 865928, 916658, 971618, 1932578, 2477476, 2558322, 3367225, 3737378, 3770258, 3964081

Offset: 1

Author

Jason Earls, Sep 21 2010

Keywords

• nonn

Examples

			9 is a term since the divisors of 9 are [1, 3, 9] and 1^1+3^2+9^3 = 739, a prime.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..100.

Programs

Maple

isA180852 := proc(n) d := sort(convert(numtheory[divisors](n),list)) ; add( op(i,d)^i,i=1..nops(d)) ; isprime(%) ; end proc:
for n from 1 do if isA180852(n) then printf("%d,\n",n) ; end if; end do: # R. J. Mathar, Sep 23 2010

Mathematica

fQ[n_] := Block[{d = Divisors@ n}, PrimeQ[ Plus @@ (d^Range@ Length@ d)]]; Select[ Range@ 4000000, fQ] (* Robert G. Wilson v, Sep 25 2010 *)
Select[Range[4*10^6],PrimeQ[Total[Divisors[#]^Range[DivisorSigma[0,#]]]]&] (* Harvey P. Dale, Nov 20 2024 *)

Extensions

Slightly more precise definition by R. J. Mathar, Sep 23 2010

a(27) onwards from Robert G. Wilson v, Sep 25 2010