cp's OEIS Frontend

A359627 Irregular table read by rows; the n-th row lists the divisors d of 2*n such that the binary expansions of d and 2*n have no common 1-bit.

%I A359627 #24 Jan 25 2024 12:35:02
%S A359627 1,1,2,1,1,2,4,1,5,1,2,3,1,1,2,4,8,1,9,1,2,10,1,1,2,3,4,6,1,1,2,1,1,2,
%T A359627 4,8,16,1,17,1,2,3,9,18,1,1,2,4,5,20,1,21,1,2,1,1,2,3,4,6,8,12,1,5,1,
%U A359627 2,1,9,1,2,4,7,1,1,2,3,1,1,2,4,8,16,32
%N A359627 Irregular table read by rows; the n-th row lists the divisors d of 2*n such that the binary expansions of d and 2*n have no common 1-bit.
%C A359627 Odd numbers share a 1-bit (2^0) with all their divisors, hence this sequence deals with even numbers.
%C A359627 The n-th row has A307314(n) terms, and sums to A359079(n).
%H A359627 <a href="/index/Di#divisors">Index entries for sequences related to divisors</a>
%F A359627 T(n,1) = 1.
%F A359627 T(n, A307314(n)) = A359708(n).
%e A359627 Table T(n, k) begins:
%e A359627     [1]
%e A359627     [1, 2]
%e A359627     [1]
%e A359627     [1, 2, 4]
%e A359627     [1, 5]
%e A359627     [1, 2, 3]
%e A359627     [1]
%e A359627     [1, 2, 4, 8]
%e A359627     [1, 9]
%e A359627     [1, 2, 10]
%e A359627     [1]
%e A359627     [1, 2, 3, 4, 6]
%e A359627     [1]
%e A359627     [1, 2]
%e A359627     [1]
%e A359627     [1, 2, 4, 8, 16]
%e A359627     [1, 17]
%o A359627 (PARI) row(n) = { select(d -> bitand(d, 2*n)==0, divisors(2*n)) }
%Y A359627 Cf. A307314 (row lengths), A359079 (row sums), A359708.
%K A359627 nonn,base,tabf
%O A359627 1,3
%A A359627 _Rémy Sigrist_, Jan 12 2023