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A343650 a(n) is the number of divisors d of n such that the product d * (n/d) can be computed without carries in binary. 2
1, 2, 2, 3, 2, 4, 2, 4, 2, 4, 2, 6, 2, 4, 4, 5, 2, 4, 2, 6, 2, 4, 2, 8, 2, 4, 4, 6, 2, 8, 2, 6, 2, 4, 2, 6, 2, 4, 2, 8, 2, 4, 2, 6, 4, 4, 2, 10, 2, 4, 4, 6, 2, 8, 2, 8, 2, 4, 2, 12, 2, 4, 6, 7, 2, 4, 2, 6, 2, 4, 2, 8, 2, 4, 2, 6, 2, 4, 2, 10, 2, 4, 2, 6, 4, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
See A343651 for the corresponding divisors.
LINKS
FORMULA
a(n) <= A000005(n).
a(2^n) = n + 1 for any n >= 0.
a(2^n - 1) = A067824(n) for any n > 0.
A001511(n) divides a(n).
EXAMPLE
For n = 18:
- we have the following divisors:
d 18/d bin(d) bin(18/d) Requires carries?
-- ---- ------ --------- -----------------
1 18 1 10010 No
2 9 10 1001 No
3 6 11 110 Yes
6 3 110 11 Yes
9 2 1001 10 No
18 1 10010 1 No
- so a(18) = #{1, 2, 9, 18} = 4.
PROG
(PARI) a(n, h=hammingweight) = my (hn=h(n)); sumdiv(n, d, hn==h(d)*h(n/d))
CROSSREFS
Sequence in context: A079243 A093640 A320538 * A327391 A365207 A083903
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Apr 24 2021
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)