A355632 Irregular triangle T(n, k), n > 0, k = 1..A121041(n), read by rows; the n-th row contains in ascending order the divisors of n whose decimal expansions appear as substrings in the decimal expansion of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 10, 1, 11, 1, 2, 12, 1, 13, 1, 14, 1, 5, 15, 1, 16, 1, 17, 1, 18, 1, 19, 2, 20, 1, 21, 2, 22, 23, 2, 4, 24, 5, 25, 2, 26, 27, 2, 28, 29, 3, 30, 1, 31, 2, 32, 3, 33, 34, 5, 35, 3, 6, 36, 37, 38, 3, 39, 4, 40, 1, 41, 2, 42, 43, 4, 44

Offset

1,2

Links

Table of n, a(n) for n=1..76.

Index entries for sequences related to decimal expansion of n

Index entries for sequences related to divisors

Formula

T(n, 1) = A121042(n).

T(n, A121041(n)) = n.

Sum_{k = 1..A121041(n)} T(n, k) = A355620(n).

Example

Triangle T(n, k) begins:
     1: [1]
     2: [2]
     3: [3]
     4: [4]
     5: [5]
     6: [6]
     7: [7]
     8: [8]
     9: [9]
    10: [1, 10]
    11: [1, 11]
    12: [1, 2, 12]
    13: [1, 13]
    14: [1, 14]
    15: [1, 5, 15]
    16: [1, 16]

Prog

(PARI) row(n, base=10) = { 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 = str(n)
    return sorted(d for d in divisors(n, generator=True) if str(d) in s)
def table(r): return [i for n in range(1, r+1) for i in row(n)]
print(table(44)) # Michael S. Branicky, Jul 11 2022

Crossrefs

Cf. A027750, A121041 (row lengths), A121042, A355620 (row sums), A355634 (binary analog).

Sequence in context: A333830 A067032 A052500 * A179933 A259433 A344487

Adjacent sequences: A355629 A355630 A355631 * A355633 A355634 A355635

Keyword

nonn,base,tabf

Author

Rémy Sigrist, Jul 11 2022

Status

approved