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

1,1

Links

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

Example

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

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 *)

Crossrefs

Sequence in context: A342473 A342619 A342471 * A075340 A031316 A335051

Adjacent sequences: A180849 A180850 A180851 * A180853 A180854 A180855

Keyword

nonn

Author

Jason Earls, Sep 21 2010

Extensions

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

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

Status

approved