A384245 Triangle read by rows: T(n, k) for 1 <= k <= n is the largest divisor of k that is an infinitary divisor of n.

1, 1, 2, 1, 1, 3, 1, 1, 1, 4, 1, 1, 1, 1, 5, 1, 2, 3, 2, 1, 6, 1, 1, 1, 1, 1, 1, 7, 1, 2, 1, 4, 1, 2, 1, 8, 1, 1, 1, 1, 1, 1, 1, 1, 9, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 3, 4, 1, 3, 1, 4, 3, 1, 1, 12, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 13

Offset: 1

Author

Amiram Eldar, May 23 2025

Keywords

• nonn
• tabl
• easy

Comments

First differs from A384047 at n = 30.

Examples

			Triangle begins:
  1
  1, 2
  1, 1, 3
  1, 1, 1, 4
  1, 1, 1, 1, 5
  1, 2, 3, 2, 1, 6
  1, 1, 1, 1, 1, 1, 7
  1, 2, 1, 4, 1, 2, 1, 8
  1, 1, 1, 1, 1, 1, 1, 1, 9
  1, 2, 1, 2, 5, 2, 1, 2, 1, 10
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10153 (first 142 rows flattened)

Crossrefs

Cf. A050873, A064379, A077609, A384047, A384246 (positions of 1's).

Programs

Mathematica

infdivs[n_] := If[n == 1, {1}, Sort@ Flatten@ Outer[Times, Sequence @@ (FactorInteger[n] /. {p_, m_Integer} :> p^Select[Range[0, m], BitOr[m, #] == m &])]];  (* Michael De Vlieger at A077609 *)
T[n_, k_] := Max[Intersection[infdivs[n], Divisors[k]]];
Table[T[n, k], {n, 1, 13}, {k, 1, n}] // Flatten

PARI

isidiv(d, f) = {if (d==1, return (1)); for (k=1, #f~, bne = binary(f[k, 2]); bde = binary(valuation(d, f[k, 1])); if (#bde < #bne, bde = concat(vector(#bne-#bde), bde)); for (j=1, #bne, if (! bne[j] && bde[j], return (0)); ); ); return (1); }
infdivs(n) = {my(f = factor(n), d = divisors(f), idiv = []); for (k=1, #d, if (isidiv(d[k], f), idiv = concat(idiv, d[k])); ); idiv; } \\ Michel Marcus at A077609
T(n, k) = vecmax(setintersect(infdivs(n), divisors(k)));