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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.
2
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
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]
MATHEMATICA
Table[Select[Divisors[n], StringContainsQ[IntegerString[n], IntegerString[#]] &], {n, 50}] (* Paolo Xausa, Jul 23 2024 *)
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
KEYWORD
nonn,base,tabf
AUTHOR
Rémy Sigrist, Jul 11 2022
STATUS
approved