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%I #28 Oct 01 2024 19:11:25
%S 0,1,34012224,8303765625,24794911296,68719476736
%N Numbers which are the sixth powers of their digit sum.
%C Solutions can have no more than 13 digits, since (13*9)^6 < 10^13.
%H René-Louis Clerc, <a href="https://hal.science/hal-04235744">Quelques nombres de Niven-Harshad particuliers</a>, 2023.
%F { k : k = A007953(k)^6}.
%F a(n) = A055577(n)^6. - _Alois P. Heinz_, Aug 24 2024
%e 68719476736 = (6+8+7+1+9+4+7+6+7+3+6)^6 = 64^6.
%o (PARI) for (k=0, sqrtnint(10^13,6), if (k^6 == sumdigits(k^6)^6, print1(k^6, ", ")); )
%Y Cf. A001014, A007953, A061209, A061210, A254000, A061211.
%Y Cf. A055577, A152147.
%K nonn,base,fini,full
%O 1,3
%A _René-Louis Clerc_, Aug 12 2024