OFFSET
1,1
COMMENTS
The majority of these numbers are squares.
The sequence of numbers j such that Sum_{i=1..k} d(i)^i = j generates the numbers 1, 130, 135, 288, 5083, 8064, 10130, ... (no more terms through 10^8).
From Michel Marcus, Mar 25 2019: (Start)
All prime squares p^2 (A001248) are terms because the partial sum 1^1 + p^2 satisfy the condition.
Up to 10^8, the terms that are not squares are: 68, 17500, 5053176.
(End)
EXAMPLE
The divisors of 68 are 1, 2, 4, 17, 34, 68; 1^1 + 2^2 + 4^3 = 69, so 68 is a term.
MAPLE
isA194269 := proc(n) local dgs , i, k; dgs := sort(convert(numtheory[divisors](n), list)) ; for k from 1 to nops(dgs) do if add(op(i, dgs)^i, i=1..k) = n+1 then return true; end if; end do; false ; end proc:
for n from 1 to 30000 do if isA194269(n) then print(n); end if; end do: # R. J. Mathar, Aug 27 2011
PROG
(PARI) isok(n) = {my(d=divisors(n), s=0); for(k=1, #d, s += d[k]^k; if (s == n+1, return (1)); if (s > n+1, break); ); } \\ Michel Marcus, Mar 25 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Aug 27 2011
STATUS
approved