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A383725 a(n) is the least number k such that omega(k) = n and the largest prime factor of k equals the sum of its remaining prime factors, where omega(k) = A001221(k).

%I A383725 #21 May 11 2025 11:56:17
%S A383725 30,3135,3570,844305,1231230,463798335,1089218130,410825520105,
%T A383725 905980145070,818186519485335,1461885412557570,2023416377587710105,
%U A383725 3676255934199278430,6175645531427513476335,14590719651042312667890,29263451149172039260325865,67794672364404337821058590
%N A383725 a(n) is the least number k such that omega(k) = n and the largest prime factor of k equals the sum of its remaining prime factors, where omega(k) = A001221(k).
%C A383725 a(n) and n have opposite parity. - _David A. Corneth_, May 08 2025
%F A383725 a(n) = (Product_{i=1..n-1} A102330(n-1,i))*A068873(n-1).
%F A383725 a(n) = A383726(n,1).
%F A383725 a(n) >= A002110(n).
%e A383725 a(3) = 30 is the smallest number having 3 distinct prime factors (namely 2, 3, and 5) such that the largest one is the sum of the others (2 + 3 = 5).
%e A383725 a(4) = 3135 is the smallest number having 4 distinct prime factors (namely 3, 5, 11 and 19) such that the largest one is the sum of the others (3 + 5 + 11 = 19).
%o A383725 (PARI) isok(k, n) = my(f=factor(k)); (omega(f)==n) && (vecsum(f[,1]) == 2*vecmax(f[,1]));
%o A383725 a(n) = my(k=1); while (!isok(k, n), k++); k; \\ _Michel Marcus_, May 08 2025
%Y A383725 Cf. A001221, A002110, A068873, A102330, A365795, A382469, A383728, A383729.
%Y A383725 First column of A383726.
%K A383725 nonn
%O A383725 3,1
%A A383725 _Paolo Xausa_, May 07 2025