A059094 -id:A059094 - cp's OEIS frontend

A053058 Cubes whose digit sum is also a cube.

0, 1, 8, 125, 512, 1000, 1331, 8000, 19683, 35937, 46656, 59319, 74088, 125000, 157464, 185193, 328509, 373248, 421875, 474552, 512000, 592704, 658503, 804357, 1000000, 1030301, 1157625, 1259712, 1331000, 1367631, 1481544, 2460375, 2628072, 3176523, 4251528, 4492125, 4741632, 5268024, 5545233, 8000000, 10503459, 10941048, 11390625, 11852352, 12326391, 12812904, 17173512, 19034163, 19683000, 20346417

Offset: 1

Felice Russo, Feb 25 2000

Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press, 2000.

Daniel Mondot, Table of n, a(n) for n = 1..10000

Intersection of A059094 and A000578.

Cf. A237525.

Select[Range[0, 200]^3, IntegerQ[(Plus@@IntegerDigits[ #])^(1/3)]&] (* Dean Hickerson, Apr 08 2002 *)
k=0;Monitor[Parallelize[While[True,If[And[IntegerQ[k^(1/3)],IntegerQ[Total[IntegerDigits[k]]^(1/3)]],Print[k]]; k++]; k], k] (* J.W.L. (Jan) Eerland, Sep 30 2024 *)

v=List();for(n=0,1e2,if(ispower(sumdigits(n^3),3), listput(v, n^3))); Vec(v) \\ Charles R Greathouse IV, Sep 20 2012

a(n) = A237525(n)^3.

More terms from James Sellers, Feb 28 2000
Edited by N. J. A. Sloane, Apr 11 2009 at the suggestion of Eric Angelini
a(33)-a(50) from J.W.L. (Jan) Eerland, Sep 30 2024

A117803 Triangular numbers for which the sum of the digits is a cube.

Original entry on oeis.org

0, 1, 10, 5778, 5886, 6786, 7875, 17766, 17955, 27495, 29646, 31878, 36585, 38781, 43956, 46665, 46971, 49455, 49770, 55278, 58653, 61776, 64980, 68265, 74691, 75078, 78606, 85491, 85905, 89253, 93096, 93528, 97461, 109278, 109746, 117855

Offset: 1

Luc Stevens (lms022(AT)yahoo.com), Apr 29 2006

			5778 is in the sequence because (1) it is a triangular number and (2) the sum of its digits 5+7+7+8=27 is a cube.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Intersection of A000217 and A059094.

Cf. A000578, A007953.

Select[Accumulate[Range[500]],IntegerQ[Power[Total[IntegerDigits[#]], (3)^-1]]&]  (* Harvey P. Dale, Dec 19 2010 *)
Select[Accumulate[Range[0,500]],IntegerQ[Surd[Total[IntegerDigits[#]],3]]&] (* Harvey P. Dale, Jan 08 2023 *)

Corrected by Harvey P. Dale, Jan 08 2023

A245021 Semiprimes whose digit sum is a perfect cube.

Original entry on oeis.org

10, 26, 35, 62, 134, 143, 161, 206, 215, 305, 314, 323, 341, 413, 422, 611, 1007, 1043, 1115, 1133, 1142, 1205, 1214, 1241, 1313, 1322, 1403, 1502, 2033, 2042, 2051, 2105, 2123, 2231, 2321, 2402, 2501, 3005, 3113, 3131, 3401, 4022, 4031, 4103, 4121, 5102, 5111

Offset: 1

K. D. Bajpai, Jul 09 2014

Semiprimes in A059094.

No a(n) have digit sum 27, because numbers with digit sum divisible by 9 are divisible by 9 and thus not semiprimes. The first member of the sequence with digit sum > 8 is 28999999 = a(1006). - Robert Israel, Jul 10 2014

			35 is in the sequence because 35 = 5 * 7 which is semiprime. Also, (3 + 5) = 8 = 2^3.
1043 is in the sequence because 1043 = 7 * 149 which is semiprime. Also, (1 + 0 + 4 + 3) = 8 = 2^3.

K. D. Bajpai, Table of n, a(n) for n = 1..1000

Cf. A001358, A007953, A059094.

N:= 10000: # to get all terms up to N
maxj:= floor((9*(1+ilog10(N)))^(1/3)):
cubes:= {seq(j^3,j=1..maxj)}:
filter:= proc(n)
local s;
if numtheory:-bigomega(n) <> 2 then return false fi;
s:= convert(convert(n,base,10),`+`);
member(s,cubes);
end proc:
select(filter, [$1..N]); # Robert Israel, Jul 10 2014

sppcQ[n_]:=PrimeOmega[n]==2&&IntegerQ[Surd[Total[IntegerDigits[n]],3]]; Select[Range[5200],sppcQ] (* Harvey P. Dale, Apr 07 2017 *)

A321881 Numbers whose sum and product of digits are cubes.

Original entry on oeis.org

0, 1, 8, 10, 80, 100, 107, 170, 206, 260, 305, 350, 404, 440, 503, 530, 602, 620, 701, 710, 800, 999, 1000, 1007, 1016, 1025, 1034, 1043, 1052, 1061, 1070, 1106, 1124, 1142, 1160, 1205, 1214, 1241, 1250, 1304, 1340, 1403, 1412, 1421, 1430, 1502, 1520, 1601, 1610, 1700

Offset: 1

Enrique Navarrete, Nov 20 2018

The first numbers in the sequence that are cubes themselves are 0,1,8,1000,8000.
a(22)=999 is the only term up to n=120 related to the cube 27 (the previous ones relate to 0,1,8).
Also, a(22)=999 is the first term that has more than one digit and consists of a single repeated digit; the next ones are 11111111 and 333333333.

			93111111111111111 (15 ones) is in the sequence since the sum and the product of the digits is 27 (a cube).
333 is not in the sequence since the product of the digits is 27 but the sum is 9 (not a cube).

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A007953, A046031, A062398, A070276, A059094, A237767.

[n:n in [0..2000]| IsPower((&+Intseq(n)), 3) and IsPower((&*Intseq(n)), 3)] // Marius A. Burtea, Jan 21 2019

filter:= proc(n) local L;
  L:= convert(n,base,10);
  simplify(convert(L,`+`)^(1/3))::integer and
  simplify(convert(L,`*`)^(1/3))::integer;
end proc:
select(filter, [$0..1000]); # Robert Israel, Jan 21 2019

cubeQ[n_] := IntegerQ[Surd[n, 3]]; aQ[n_] := cubeQ[Plus @@ IntegerDigits[n]] &&
cubeQ[Times @@ IntegerDigits[n]]; Select[Range[0, 3000], aQ] (* Amiram Eldar, Nov 20 2018 *)

isok(n) = my(d=digits(n)); ispower(vecsum(d), 3) && ispower(vecprod(d), 3); \\ Michel Marcus, Nov 29 2018

A331203 Numbers k such that k/(digsum(k)) is an integer cube.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 72, 243, 320, 486, 512, 640, 704, 832, 960, 1000, 1088, 1125, 2000, 2401, 3000, 3430, 4000, 4116, 4802, 5000, 5145, 5831, 6000, 6174, 6517, 6860, 7000, 7546, 8000, 8575, 8918, 9000, 9216, 9947, 19683, 35152, 35937, 41743, 43940, 46137

Offset: 1

K. D. Bajpai, Jan 12 2020

If m belongs to the sequence, then 1000*m also belongs to the sequence. - Rémy Sigrist, Jan 12 2020

			a(11) = 243: 243/(2 + 4 + 3) = 27 = 3^3.
a(12) = 320: 320/(3 + 2 + 0) = 64 = 4^3.

Cf. A001102, A005349, A007953, A028839, A059094.

[n : n in[1 .. 1000] | IsIntegral((n/(&+Intseq(n)))^(1/3))];

Select[Range[100000], IntegerQ[CubeRoot[#/Total[IntegerDigits[#]]]] &]

is(n) = my (k=n/sumdigits(n)); type(k)==type(42) && ispower(k,3) \\ Rémy Sigrist, Jan 12 2020

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A053058 Cubes whose digit sum is also a cube.

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A117803 Triangular numbers for which the sum of the digits is a cube.

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A245021 Semiprimes whose digit sum is a perfect cube.

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A321881 Numbers whose sum and product of digits are cubes.

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Magma

Maple

Mathematica

PARI

A331203 Numbers k such that k/(digsum(k)) is an integer cube.

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Programs

Magma

Mathematica

PARI