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%I #12 Feb 12 2023 03:18:18
%S 3,6,11,14,19,21,22,30,38,39,42,46,47,51,55,56,60,62,66,67,69,70,71,
%T 75,77,78,79,83,84,86,92,93,94,95,102,103,105,107,110,114,115,118,120,
%U 123,131,138,139,142,143,147,151,154,156,158,159,163,165,166,167,168,175
%N Numbers that require three powerful numbers (definition 1) to sum to them.
%H Amiram Eldar, <a href="/A063275/b063275.txt">Table of n, a(n) for n = 1..10000</a>
%e The powerful numbers (A001694) start 1, 4, 8, 9, ... Now 11 = 1+1+9 and is not the sum of fewer terms, so 11 is in the sequence.
%t With[{m = 200}, pow = Select[Range[m], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 1 &]; s2 = Select[Union[Plus @@@ Tuples[pow, {2}]], # <= m &]; s3 = Select[Union[Plus @@@ Tuples[pow, {3}]], # <= m &]]; Complement[s3, pow, s2] (* _Amiram Eldar_, Feb 12 2023 *)
%Y Cf. A001694, A056828, A063274.
%K nonn
%O 1,1
%A _Jud McCranie_, Jul 13 2001
%E Offset corrected by _Amiram Eldar_, Feb 12 2023