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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.
3
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 *)
CROSSREFS
Sequence in context: A342473 A342619 A342471 * A075340 A031316 A335051
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