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

1,3

Comments

First differs from A384047 at n = 30.

Links

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

Example

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

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

Prog

(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)));

Crossrefs

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

Sequence in context: A216764 A165430 A384047 * A334215 A164823 A167269

Adjacent sequences: A384242 A384243 A384244 * A384246 A384247 A384248

Keyword

nonn,tabl,easy

Author

Amiram Eldar, May 23 2025

Status

approved