A355634 Irregular triangle T(n, k), n > 0, k = 1..A093640(n), read by rows; the n-th row contains in ascending order the divisors of n whose binary expansions appear as substrings in the binary expansion of n.
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, 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
Examples
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, 15]
16: [1, 2, 4, 8, 16]
Links
- Paolo Xausa, Table of n, a(n) for n = 1..10019 (rows 1..2000 of the triangle, flattened).
- Index entries for sequences related to binary expansion of n
- Index entries for sequences related to divisors
Programs
-
Mathematica
Table[Select[Divisors[n], StringContainsQ[IntegerString[n, 2], IntegerString[#, 2]] &], {n, 50}] (* Paolo Xausa, Jul 23 2024 *) -
PARI
row(n, base=2) = { my (d=digits(n, base), s=setbinop((i, j) -> fromdigits(d[i..j], base), [1..#d]), v=0); select(v -> v && n%v==0, s) } -
Python
from sympy import divisors def row(n): s = bin(n)[2:] return sorted(d for d in divisors(n, generator=True) if bin(d)[2:] in s) def table(r): return [i for n in range(1, r+1) for i in row(n)] print(table(25)) # Michael S. Branicky, Jul 11 2022