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A194269 Numbers j such that Sum_{i=1..k} d(i)^i = j+1 for some k where d(i) is the sorted list of divisors of j. 1
4, 9, 25, 49, 68, 121, 169, 289, 361, 529, 841, 961, 1369, 1681, 1849, 2209, 2809, 3481, 3721, 4489, 5041, 5329, 6241, 6889, 7921, 9409, 10201, 10609, 11449, 11881, 12769, 16129, 17161, 17500, 18769, 19321, 22201, 22801, 24649, 26569, 27889 (list; graph; refs; listen; history; text; internal format)
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)

LINKS

Table of n, a(n) for n=1..41.

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

Cf. A001248, A064510, A180851.

Sequence in context: A069557 A230312 A306043 * A130283 A065739 A053704

Adjacent sequences:  A194266 A194267 A194268 * A194270 A194271 A194272

KEYWORD

nonn

AUTHOR

Michel Lagneau, Aug 27 2011

STATUS

approved

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Last modified October 17 14:20 EDT 2019. Contains 328113 sequences. (Running on oeis4.)