A393541 - OEIS

%I #32 Mar 21 2026 10:02:17

%S 30,690,210,420,4830,4620,9660,39270,90090,60060,106260,180180,318780,

%T 510510,1492260,1531530,1021020,1381380,3063060,5419260,4144140,

%U 12432420,9699690,29609580,29099070,35225190,19399380,26246220,38798760,77597520,70450380,78738660

%N Least composite divisible by the sum of three of its distinct prime divisors in exactly n different ways.

%C All the numbers found are divisible by 30.

%C Terms of the sequence which can be divided by all the possible sums of 3 of their different prime divisors are 30, 420, ...

%H Giovanni Resta, <a href="/A393541/b393541.txt">Table of n, a(n) for n = 1..100</a> (first 45 terms from Paolo P. Lava).

%e a(4) = 420 because its prime factors are 2, 3, 5, 7 and

%e   420/(2+3+5) = 42;  420/(2+3+7) = 35;  420/(2+5+7) = 30;  420/(3+5+7) = 28.

%e a(10) = 60060 because its prime factors are 2, 3, 5, 7, 11, 13 and

%e   60060 /(2+3+5) = 6006;  60060 /(2+3+7) = 5005;  60060 /(2+5+7) = 4290;  60060 /(2+5+13) = 3003;

%e   60060 /(2+7+11) = 3003;  60060 /(2+7+13) = 2730;  60060/(2+11+13) = 2310;  60060 /(3+5+7) = 4004;

%e   60060 /(3+5+13) = 2860;  60060 /(3+7+11) = 2860.

%t a[n_]:=Module[{k=4},While[ Total[Boole[Divisible[k,Total/@Subsets[First/@FactorInteger[k],{3}]]]]!=n,k++];k];Array[a,15] (* _James C. McMahon_, Mar 14 2026 *)

%Y Cf. A393540.

%K nonn

%O 1,1

%A _Paolo P. Lava_, Mar 02 2026