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%I #17 Sep 06 2023 01:39:57
%S 2,3,4,5,7,8,9,11,13,16,17,19,23,25,29,31,32,37,41,43,47,53,59,61,67,
%T 71,73,79,103,107,109,113
%N Prime powers q for which f(g(m(q))) = m(q), where f = A051703, g = A008475 and m = A003418.
%C These functions are defined for all natural numbers > 1 by: g(x) = Sum (p_j^k_j) where x = Product (p_j^k_j) is prime factorization of x (A008475); f(n) = max{x:g(x)=n} (A051703); m(n) = lcm(1,2,3,...,n) (A003418).
%C There are no more prime powers in the list <= 199. Conjecture: The sequence is finite, i.e., f(g(m(q))) > m(q) for sufficiently great prime powers q.
%C No other terms below 409. - _Max Alekseyev_, Sep 05 2023
%H D. W. Wilson, <a href="http://mathforum.org/epigone/sci.math/gingpholkhan">Answers to sci.math questions</a>
%e 27 is not in the list because m(27) = 2^4*3^3*5^2*7*11*13*17*19*23, g(m(27))=158, f(158) = 3*5*7*11*13*17*19*23*29*31 > m(27).
%Y Cf. A000961, A003418, A008475, A051703.
%K nonn,more
%O 1,1
%A _Vladeta Jovovic_, May 01 2000
%E Offset changed to 1 by _Jinyuan Wang_, Mar 16 2020