cp's OEIS Frontend

A321881 Numbers whose sum and product of digits are cubes.

%I A321881 #30 Sep 08 2022 08:46:23
%S A321881 0,1,8,10,80,100,107,170,206,260,305,350,404,440,503,530,602,620,701,
%T A321881 710,800,999,1000,1007,1016,1025,1034,1043,1052,1061,1070,1106,1124,
%U A321881 1142,1160,1205,1214,1241,1250,1304,1340,1403,1412,1421,1430,1502,1520,1601,1610,1700
%N A321881 Numbers whose sum and product of digits are cubes.
%C A321881 The first numbers in the sequence that are cubes themselves are 0,1,8,1000,8000.
%C A321881 a(22)=999 is the only term up to n=120 related to the cube 27 (the previous ones relate to 0,1,8).
%C A321881 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.
%H A321881 Robert Israel, <a href="/A321881/b321881.txt">Table of n, a(n) for n = 1..10000</a>
%e A321881 93111111111111111 (15 ones) is in the sequence since the sum and the product of the digits is 27 (a cube).
%e A321881 333 is not in the sequence since the product of the digits is 27 but the sum is 9 (not a cube).
%p A321881 filter:= proc(n) local L;
%p A321881   L:= convert(n,base,10);
%p A321881   simplify(convert(L,`+`)^(1/3))::integer and
%p A321881   simplify(convert(L,`*`)^(1/3))::integer;
%p A321881 end proc:
%p A321881 select(filter, [$0..1000]); # _Robert Israel_, Jan 21 2019
%t A321881 cubeQ[n_] := IntegerQ[Surd[n, 3]]; aQ[n_] := cubeQ[Plus @@ IntegerDigits[n]] &&
%t A321881 cubeQ[Times @@ IntegerDigits[n]]; Select[Range[0, 3000], aQ] (* _Amiram Eldar_, Nov 20 2018 *)
%o A321881 (PARI) isok(n) = my(d=digits(n)); ispower(vecsum(d), 3) && ispower(vecprod(d), 3); \\ _Michel Marcus_, Nov 29 2018
%o A321881 (Magma) [n:n in [0..2000]| IsPower((&+Intseq(n)), 3) and IsPower((&*Intseq(n)), 3)] // _Marius A. Burtea_, Jan 21 2019
%Y A321881 Cf. A007953, A046031, A062398, A070276, A059094, A237767.
%K A321881 nonn,base
%O A321881 1,3
%A A321881 _Enrique Navarrete_, Nov 20 2018