A335440 Lexicographically earliest sequence of distinct positive terms such that two distinct terms differ by at least 3 prime factors.

1, 8, 18, 50, 60, 64, 81, 98, 105, 144, 225, 242, 308, 338, 400, 429, 441, 480, 512, 546, 578, 625, 648, 722, 756, 784, 884, 935, 969, 1058, 1089, 1122, 1152, 1190, 1225, 1235, 1428, 1430, 1458, 1463, 1485, 1521, 1547, 1682, 1748, 1800, 1820, 1922, 1936, 2001

Offset

1,2

Comments

In other words, for any distinct m and n, let a(m)/a(n) = u/v in reduced form, then bigomega(u) + bigomega(v) >= 3 (where bigomega corresponds to A001222(n), the number of distinct prime factors of n with multiplicity).

The variant where distinct terms differ by at least 1 prime factor simply corresponds to the positive numbers.

The variant where distinct terms differ by at least 2 prime factors corresponds to A028260.

No term is prime nor the square of a prime.

This sequence has similarities with A075926 and A333568; here we consider prime factors, there digits.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, C program for A335440

Example

The first terms, alongside their p-adic valuations for p = 2..11 (with dots instead of zeros), are:
  n   a(n)  v2  v3  v5  v7  v11
  --  ----  --  --  --  --  ---
   1     1   .   .   .   .    .
   2     8   3   .   .   .    .
   3    18   1   2   .   .    .
   4    50   1   .   2   .    .
   5    60   2   1   1   .    .
   6    64   6   .   .   .    .
   7    81   .   4   .   .    .
   8    98   1   .   .   2    .
   9   105   .   1   1   1    .
  10   144   4   2   .   .    .
  11   225   .   2   2   .    .
  12   242   1   .   .   .    2
  13   308   2   .   .   1    1

Prog

(C) See Links section.

Crossrefs

Cf. A001222, A028260, A075926, A333568.

Sequence in context: A034714 A153388 A109988 * A066721 A079704 A341528

Adjacent sequences: A335437 A335438 A335439 * A335441 A335442 A335443

Keyword

nonn

Author

Rémy Sigrist, Jun 10 2020

Status

approved