OFFSET
1,1
COMMENTS
All the numbers found are divisible by 30.
Terms of the sequence which can be divided by all the possible sums of 3 of their different prime divisors are 30, 420, ...
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..100 (first 45 terms from Paolo P. Lava).
EXAMPLE
a(4) = 420 because its prime factors are 2, 3, 5, 7 and
420/(2+3+5) = 42; 420/(2+3+7) = 35; 420/(2+5+7) = 30; 420/(3+5+7) = 28.
a(10) = 60060 because its prime factors are 2, 3, 5, 7, 11, 13 and
60060 /(2+3+5) = 6006; 60060 /(2+3+7) = 5005; 60060 /(2+5+7) = 4290; 60060 /(2+5+13) = 3003;
60060 /(2+7+11) = 3003; 60060 /(2+7+13) = 2730; 60060/(2+11+13) = 2310; 60060 /(3+5+7) = 4004;
60060 /(3+5+13) = 2860; 60060 /(3+7+11) = 2860.
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Mar 02 2026
STATUS
approved