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%I #21 Apr 12 2024 09:49:05
%S 4,6,9,38,39,49,69,169,278,289,299,489,589,689,699,799,899,2899,3899,
%T 4989,5899,5999,6999,7999,9899,19999,29999,48999,58999,68999,69999,
%U 88999,99899,299899,398999,589989,589999,689999,798999,889999,899999,2899999,3899999
%N The semiprimes which set new records for the sum of their decimal digits.
%C The semiprimes that set new records in A175013. New records of digit sums of 4, 6, 9, 11, 12, 13, 15, 16, 17,.. are set by the semiprimes 4, 6, 9, 38, 39, 49, 69,...
%H K. D. Bajpai, <a href="/A257652/b257652.txt">Table of n, a(n) for n = 1..64</a>
%e a(4) = 38 = 2 * 19, which is a semiprime with sum of digits = 3 + 8 = 11.
%e a(5) = 39 = 3 * 13, which is a semiprime with sum of digits = 3 + 9 = 12. Since 12 > 11, 38 and 39 are in list.
%t t = {}; s = 0; Do[If[(x = Total[IntegerDigits[n]]) > s && PrimeOmega[n] == 2, AppendTo[t, n]; s = x], {n, 1000000}];t
%t DeleteDuplicates[{#,Total[IntegerDigits[#]]}&/@Select[Range[4*10^6],PrimeOmega[#] == 2&],GreaterEqual[ #1[[2]],#2[[2]]]&][[;;,1]] (* _Harvey P. Dale_, Apr 12 2024 *)
%Y Cf. A175013, A068809, A246569.
%Y Subsequence of A213653.
%K nonn,base
%O 1,1
%A _K. D. Bajpai_, Jul 25 2015