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%I #7 Jul 11 2022 16:10:20
%S 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,
%T 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,
%U 34,5,35,3,6,36,37,38,3,39,4,40,1,41,2,42,43,4,44
%N 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.
%H <a href="/index/De#decimal_expansion">Index entries for sequences related to decimal expansion of n</a>
%H <a href="/index/Di#divisors">Index entries for sequences related to divisors</a>
%F T(n, 1) = A121042(n).
%F T(n, A121041(n)) = n.
%F Sum_{k = 1..A121041(n)} T(n, k) = A355620(n).
%e Triangle T(n, k) begins:
%e 1: [1]
%e 2: [2]
%e 3: [3]
%e 4: [4]
%e 5: [5]
%e 6: [6]
%e 7: [7]
%e 8: [8]
%e 9: [9]
%e 10: [1, 10]
%e 11: [1, 11]
%e 12: [1, 2, 12]
%e 13: [1, 13]
%e 14: [1, 14]
%e 15: [1, 5, 15]
%e 16: [1, 16]
%o (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) }
%o (Python)
%o from sympy import divisors
%o def row(n):
%o s = str(n)
%o return sorted(d for d in divisors(n, generator=True) if str(d) in s)
%o def table(r): return [i for n in range(1, r+1) for i in row(n)]
%o print(table(44)) # _Michael S. Branicky_, Jul 11 2022
%Y Cf. A027750, A121041 (row lengths), A121042, A355620 (row sums), A355634 (binary analog).
%K nonn,base,tabf
%O 1,2
%A _Rémy Sigrist_, Jul 11 2022
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