cp's OEIS Frontend

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.

%I A343651 #9 Apr 25 2021 15:14:52
%S A343651 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 A343651 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 A343651 20,1,21,1,2,11,22,1,23,1,2,3,4,6,8,12,24,1,25
%N 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.
%H A343651 Rémy Sigrist, <a href="/A343651/b343651.txt">Table of n, a(n) for n = 1..4788</a> (rows for n = 1..1024)
%H A343651 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A343651 <a href="/index/Di#divisors">Index entries for sequences related to divisors</a>
%F A343651 T(n, 1) = 1.
%F A343651 T(n, A343650(n)) = n.
%e A343651 Triangle T(n, k) begins:
%e A343651      1:     [1]
%e A343651      2:     [1, 2]
%e A343651      3:     [1, 3]
%e A343651      4:     [1, 2, 4]
%e A343651      5:     [1, 5]
%e A343651      6:     [1, 2, 3, 6]
%e A343651      7:     [1, 7]
%e A343651      8:     [1, 2, 4, 8]
%e A343651      9:     [1, 9]
%e A343651     10:     [1, 2, 5, 10]
%e A343651     11:     [1, 11]
%e A343651     12:     [1, 2, 3, 4, 6, 12]
%e A343651     13:     [1, 13]
%e A343651     14:     [1, 2, 7, 14]
%e A343651     15:     [1, 3, 5, 15]
%o A343651 (PARI) row(n, h=hammingweight) = my (hn=h(n)); select(d -> hn==h(d)*h(n/d), divisors(n))
%Y A343651 Cf. A343650.
%K A343651 nonn,tabf,base
%O A343651 1,3
%A A343651 _Rémy Sigrist_, Apr 25 2021