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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.
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%I #9 Apr 25 2021 15:14:52

%S 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,

%T 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,

%U 20,1,21,1,2,11,22,1,23,1,2,3,4,6,8,12,24,1,25

%N 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.

%H Rémy Sigrist, <a href="/A343651/b343651.txt">Table of n, a(n) for n = 1..4788</a> (rows for n = 1..1024)

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Di#divisors">Index entries for sequences related to divisors</a>

%F T(n, 1) = 1.

%F T(n, A343650(n)) = n.

%e Triangle T(n, k) begins:

%e 1: [1]

%e 2: [1, 2]

%e 3: [1, 3]

%e 4: [1, 2, 4]

%e 5: [1, 5]

%e 6: [1, 2, 3, 6]

%e 7: [1, 7]

%e 8: [1, 2, 4, 8]

%e 9: [1, 9]

%e 10: [1, 2, 5, 10]

%e 11: [1, 11]

%e 12: [1, 2, 3, 4, 6, 12]

%e 13: [1, 13]

%e 14: [1, 2, 7, 14]

%e 15: [1, 3, 5, 15]

%o (PARI) row(n, h=hammingweight) = my (hn=h(n)); select(d -> hn==h(d)*h(n/d), divisors(n))

%Y Cf. A343650.

%K nonn,tabf,base

%O 1,3

%A _Rémy Sigrist_, Apr 25 2021