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A345874
a(n) is the number of distinct pairs of positive integers (u, v) such that A065157(u, v) = n.
1
1, 2, 2, 3, 2, 3, 2, 4, 2, 4, 2, 4, 2, 3, 3, 5, 2, 4, 2, 5, 2, 3, 2, 5, 2, 3, 3, 4, 2, 4, 2, 6, 2, 4, 2, 6, 2, 3, 2, 6, 2, 4, 2, 4, 3, 3, 2, 6, 2, 3, 3, 4, 2, 5, 2, 5, 2, 3, 2, 5, 2, 3, 4, 7, 2, 4, 2, 6, 2, 3, 2, 7, 2, 4, 2, 4, 2, 3, 2, 7, 2, 4, 2, 5, 3, 3, 2
OFFSET
1,2
COMMENTS
If A065157(u, v) = n then u is a divisor of n.
FORMULA
a(n) <= A000005(n).
a(n) >= 2 for any n > 1 (as A065157(1, n) = A065157(n, 1) = n).
a(2^k) = k + 1 for any k >= 0.
a(2^k - 1) = A000005(k) for any k > 0.
EXAMPLE
For n = 10:
- the table A065157(u, v) begins (with terms > 10 replaced by dots):
u\v| 1 2 3 4 5 6 7 8 9 10
---+----------------------------------
1| 1 2 3 4 5 6 7 8 9 10
2| 2 4 10 8 . . . . . .
3| 3 6 . . . . . . . .
4| 4 8 . . . . . . . .
5| 5 10 . . . . . . . .
6| 6 . . . . . . . . .
7| 7 . . . . . . . . .
8| 8 . . . . . . . . .
9| 9 . . . . . . . . .
10| 10 . . . . . . . . .
- the value 10 appears 4 times,
- so a(10) = 4.
PROG
(PARI) See Links section.
CROSSREFS
Sequence in context: A087458 A052180 A065151 * A338720 A320013 A299990
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jun 27 2021
STATUS
approved