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%I #16 Feb 01 2024 20:06:38
%S 1,1,2,3,8,1,12,3,16,3,30,2,48,20,6,15,80,6,108,6,20,63,176,1,24,50,
%T 50,18
%N Smallest number of powers of n with positive exponents that sum to a factorial.
%C For n > 1, a(n) is the smallest base-n digit sum of m! for m >= A002034(n). Values m = A002034(n) correspond to A354861, and so a(n) <= A354861(n). The two sequences share many terms but differ: a(14) = 20 < 22 = A354861(14).
%C The sequence likely continues as 280, 4, 330, ...
%e a(7) = 12 since 7! = 2*7^4 + 4*7^2 + 6*7^1 with 2+4+6=12, and the sum of 11 or less powers of 7 cannot be a multiple of 48.
%Y Cf. A000142, A002034, A354861.
%K nonn,hard,more
%O 1,3
%A _Max Alekseyev_, Jun 08 2022
%E a(17)-a(18) from _Jinyuan Wang_, Jun 10 2022
%E a(19)-a(28) from _Max Alekseyev_, Feb 01 2024
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