login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A343651
Irregular triangle T(n, k), n > 0, k = 1..A343650(n), read by rows; the n-th row lists the divisors d of n such that the product d * (n/d) can be computed without carries in binary.
2
1, 1, 2, 1, 3, 1, 2, 4, 1, 5, 1, 2, 3, 6, 1, 7, 1, 2, 4, 8, 1, 9, 1, 2, 5, 10, 1, 11, 1, 2, 3, 4, 6, 12, 1, 13, 1, 2, 7, 14, 1, 3, 5, 15, 1, 2, 4, 8, 16, 1, 17, 1, 2, 9, 18, 1, 19, 1, 2, 4, 5, 10, 20, 1, 21, 1, 2, 11, 22, 1, 23, 1, 2, 3, 4, 6, 8, 12, 24, 1, 25
OFFSET
1,3
FORMULA
T(n, 1) = 1.
T(n, A343650(n)) = n.
EXAMPLE
Triangle T(n, k) begins:
1: [1]
2: [1, 2]
3: [1, 3]
4: [1, 2, 4]
5: [1, 5]
6: [1, 2, 3, 6]
7: [1, 7]
8: [1, 2, 4, 8]
9: [1, 9]
10: [1, 2, 5, 10]
11: [1, 11]
12: [1, 2, 3, 4, 6, 12]
13: [1, 13]
14: [1, 2, 7, 14]
15: [1, 3, 5, 15]
PROG
(PARI) row(n, h=hammingweight) = my (hn=h(n)); select(d -> hn==h(d)*h(n/d), divisors(n))
CROSSREFS
Cf. A343650.
Sequence in context: A027750 A275055 A254679 * A355634 A275280 A319845
KEYWORD
nonn,tabf,base
AUTHOR
Rémy Sigrist, Apr 25 2021
STATUS
approved