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).

30, 3135, 3570, 844305, 1231230, 463798335, 1089218130, 410825520105, 905980145070, 818186519485335, 1461885412557570, 2023416377587710105, 3676255934199278430, 6175645531427513476335, 14590719651042312667890, 29263451149172039260325865, 67794672364404337821058590

Offset: 3

Author

Paolo Xausa, May 07 2025

Keywords

• nonn

Comments

a(n) and n have opposite parity. - David A. Corneth, May 08 2025

Examples

			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).
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).
		

Crossrefs

Cf. A001221, A002110, A068873, A102330, A365795, A382469, A383728, A383729.

First column of A383726.

Programs

PARI

isok(k, n) = my(f=factor(k)); (omega(f)==n) && (vecsum(f[,1]) == 2*vecmax(f[,1]));
a(n) = my(k=1); while (!isok(k, n), k++); k; \\ Michel Marcus, May 08 2025

Formula

a(n) = (Product_{i=1..n-1} A102330(n-1,i))*A068873(n-1).

a(n) = A383726(n,1).

a(n) >= A002110(n).