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A178204 Smith numbers of order 6; composite numbers n such that sum of digits^6 equal sum of digits^6 of its prime factors without the numbers in A176670 that have the same digits as its prime factors (without the zero digits).

%I A178204 #15 Feb 16 2025 08:33:12
%S A178204 40844882,113986781,130852098,141176320,168137185,170774472,178180163,
%T A178204 181681157,181693781,183161897,187117638,215149451,261666000,
%U A178204 284804842,294557945,307711074,335524949,337194240,344552927,347391040,355318188,358831104,368657536
%N A178204 Smith numbers of order 6; composite numbers n such that sum of digits^6 equal sum of digits^6 of its prime factors without the numbers in A176670 that have the same digits as its prime factors (without the zero digits).
%H A178204 Donovan Johnson, <a href="/A178204/b178204.txt">Table of n, a(n) for n = 1..1000</a>
%H A178204 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/SmithNumber.html">Smith Number</a>
%e A178204 a(4) = 141176320 = 2^9*5*55147;
%e A178204 3*1^6+2^6+3^6+4^6+6^6+7^6 = 1^6+9*2^6+4^6+3*5^6+7^6 = 169197
%t A178204 fQ[n_] := Block[{id = Sort@ IntegerDigits@ n, fid = Sort@ Flatten[ IntegerDigits@ Table[ #[[1]], {#[[2]]}] & /@ FactorInteger@ n]}, While[ id[[1]] == 0, id = Drop[id, 1]]; While[ fid[[1]] == 0, fid = Drop[fid, 1]]; id != fid && Plus @@ (id^6) == Plus @@ (fid^6)]; k = 2; lst = {}; While[k < 50000001, If[fQ@ k, AppendTo[ lst, k]; Print@ k]; k++]; lst
%Y A178204 Cf. A006753 (Smith numbers), A176670, A174460, A178213, A178193, A178203.
%K A178204 nonn,base
%O A178204 1,1
%A A178204 _Paul Weisenhorn_, Dec 19 2010
%E A178204 Example corrected by _Donovan Johnson_, Jan 02 2013