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A340048 Numbers that are the sum of a cube s and a fourth power t such that 0 < s <= t. 0
2, 17, 24, 82, 89, 108, 145, 257, 264, 283, 320, 381, 472, 626, 633, 652, 689, 750, 841, 968, 1137, 1297, 1304, 1323, 1360, 1421, 1512, 1639, 1808, 2025, 2296, 2402, 2409, 2428, 2465, 2526, 2617, 2744, 2913, 3130, 3401, 3732, 4097, 4104, 4123, 4129, 4160, 4221, 4312 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Contains the entries of A340050 and numbers like 2, 8192, 1062882,.. which are 2 times 12th powers (A008456). - R. J. Mathar, Jan 05 2021

LINKS

Table of n, a(n) for n=1..49.

EXAMPLE

24 is in the sequence since 2^3 + 2^4 = 8 + 16 = 24, where 0 < 8 <= 16.

MAPLE

isA340048 := proc(n)

    local t, s3 ;

    for t from 0 do

        s3 := n-t^4 ;

        if s3 <= 0 then

            return false ;

        elif s3 <= t^4 and isA000578(s3) then

            return true;

        end if;

    end do:

end proc:

for n from 1 do

    if isA340048(n) then

        printf("%d, \n", n) ;

    end if;

end do: # R. J. Mathar, Jan 05 2021

MATHEMATICA

Table[If[Sum[(Floor[i^(1/3)] - Floor[(i - 1)^(1/3)]) (Floor[(n - i)^(1/4)] - Floor[(n - i - 1)^(1/4)]), {i, Floor[n/2]}] > 0, n, {}], {n, 1000}] // Flatten

PROG

(Python)

def aupto(lim):

  cubes = [i**3 for i in range(1, int(lim**(1/3))+2)]

  fours = [i**4 for i in range(1, int(lim**(1/4))+2)]

  return sorted(s+t for s in cubes for t in fours if t >= s and s+t <= lim)

print(aupto(4312)) # Michael S. Branicky, Feb 17 2021

CROSSREFS

Cf. A010057.

Cf. A008456, A340050.

Sequence in context: A049562 A107137 A086322 * A164275 A284646 A270344

Adjacent sequences:  A340045 A340046 A340047 * A340049 A340050 A340052

KEYWORD

nonn,changed

AUTHOR

Wesley Ivan Hurt, Dec 26 2020

STATUS

approved

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Last modified February 25 14:40 EST 2021. Contains 341609 sequences. (Running on oeis4.)