A180852 - OEIS

%I #12 Dec 15 2017 17:37:11

%S 2,9,18,5618,7744,10000,28561,30258,34322,40000,46225,165649,200978,

%T 249218,258064,310472,370881,393129,425042,438244,542882,595984,

%U 865928,916658,971618,1932578,2477476,2558322,3367225,3737378,3770258,3964081

%N 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.

%H Robert G. Wilson v, <a href="/A180852/b180852.txt">Table of n, a(n) for n = 1..100</a>.

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

%p isA180852 := proc(n) d := sort(convert(numtheory[divisors](n),list)) ; add( op(i,d)^i,i=1..nops(d)) ; isprime(%) ; end proc:

%p for n from 1 do if isA180852(n) then printf("%d,\n",n) ; end if; end do: # _R. J. Mathar_, Sep 23 2010

%t fQ[n_] := Block[{d = Divisors@ n}, PrimeQ[ Plus @@ (d^Range@ Length@ d)]]; Select[ Range@ 4000000, fQ] (* _Robert G. Wilson v_, Sep 25 2010 *)

%K nonn

%O 1,1

%A _Jason Earls_, Sep 21 2010

%E Slightly more precise definition by _R. J. Mathar_, Sep 23 2010

%E a(27) onwards from _Robert G. Wilson v_, Sep 25 2010