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A335440
Lexicographically earliest sequence of distinct positive terms such that two distinct terms differ by at least 3 prime factors.
1
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
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
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jun 10 2020
STATUS
approved