A393540 Least composite divisible by the sum of two of its distinct prime divisors in exactly n different ways.

30, 120, 210, 420, 840, 2520, 10920, 16380, 32760, 65520, 180180, 240240, 360360, 1506960, 720720, 5969040, 4084080, 6126120, 16576560, 12252240, 27387360, 93933840, 77597520, 140900760, 116396280, 281801520, 232792560, 465585120, 1784742960, 3569485920, 3608284680

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 2 of their different prime divisors are 2520, 65520, 720720, 27387360, 465585120, 53542288800, ...

binomial(omega(a(n)), 2) >= n. - David A. Corneth, Mar 06 2026

Links

Paolo P. Lava, Table of n, a(n) for n = 1..50

Example

a(4) = 420 because its prime factors are 2, 3, 5, 7 and
  420/(2+3) = 84; 420/(2+5) = 60; 420/(3+7) = 42; 420/(5+7) = 35.
a(10) = 65520 because its prime factors are 2, 3, 5, 7, 13 and
  65520/(2+3) = 13104;  65520/(2+5) = 9360;  65520/(2+7) = 7280;  65520/(2+13) = 4368;
  65520/(3+5) = 8190;  65520/(3+7) = 6552;  65520/(3+13) = 4095;  65520/(5+7) = 5460;
  65520/(5+13) = 3640;  65520/(7+13) = 3276.

Crossrefs

Cf. A393541

Sequence in context: A383677 A246766 A112955 * A244636 A290391 A277451

Adjacent sequences: A393536 A393537 A393539 * A393541 A393542 A393543

Keyword

nonn

Author

Paolo P. Lava, Mar 02 2026

Extensions

a(24) onward by Giovanni Resta, Mar 05 2026

Status

approved