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%I #60 Dec 06 2021 03:13:36
%S 36,1009,12384,82278,746992,5401404,15685704,26936064,137763072,
%T 251066304,857520000,618817536,3032856000,2050677000,6100691904,
%U 36013192704,16405416000,96569712000,48805535232,131243328000,611996202000,201153672000
%N Smallest number which can be decomposed into exactly n sums of three distinct positive cubes, but cannot be decomposed into more than one such sum containing the same cube.
%C No cube should appear in two or more sums. 5104 = 15^3 + 10^3 + 9^3 = 15^3 + 12^3 + 1^3 = 16^3 + 10^3 + 2^3 is not a(3), because 15^3 appears in more than one sum.
%H Gleb Ivanov, <a href="/A347362/a347362.txt">Rust program for large terms</a>.
%H Gleb Ivanov, <a href="/A347362/a347362.py.txt">Python program</a>.
%e a(1) = 36 = 1^3 + 2^3 + 3^3.
%e a(2) = 1009 = 1^3 + 2^3 + 10^3 = 4^3 + 6^3 + 9^3.
%e a(3) = 12384 = 1^3 + 6^3 + 23^3 = 2^3 + 12^3 + 22^3 = 15^3 + 16^3 + 17^3.
%t Monitor[Do[k=1;While[Length@Union@Flatten[p=PowersRepresentations[k,3,3]]!=n*3||Length@p!=n||MemberQ[Flatten@p,0],k++];Print@k,{n,10}],k] (* _Giorgos Kalogeropoulos_, Sep 03 2021 *)
%Y Cf. A025333, A025419, A025469, A025398.
%Y Cf. A343968, A343967, A345088, A345087, A345119, A345152.
%K nonn,hard,more
%O 1,1
%A _Gleb Ivanov_, Aug 29 2021
%E a(13)-a(15) from _Jon E. Schoenfield_, Sep 02 2021
%E a(16)-a(22) from _Gleb Ivanov_, Sep 12 2021
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