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A321881
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Numbers whose sum and product of digits are cubes.
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1
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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
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OFFSET
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1,3
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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).
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MAPLE
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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:
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MATHEMATICA
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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 *)
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PROG
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(PARI) isok(n) = my(d=digits(n)); ispower(vecsum(d), 3) && ispower(vecprod(d), 3); \\ Michel Marcus, Nov 29 2018
(Magma) [n:n in [0..2000]| IsPower((&+Intseq(n)), 3) and IsPower((&*Intseq(n)), 3)] // Marius A. Burtea, Jan 21 2019
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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