cp's OEIS Frontend

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.

%I A384245 #8 May 27 2025 01:17:42
%S A384245 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,
%T A384245 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,
%U A384245 1,3,4,1,3,1,4,3,1,1,12,1,1,1,1,1,1,1,1,1,1,1,1,13
%N 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.
%C A384245 First differs from A384047 at n = 30.
%H A384245 Amiram Eldar, <a href="/A384245/b384245.txt">Table of n, a(n) for n = 1..10153</a> (first 142 rows flattened)
%e A384245 Triangle begins:
%e A384245   1
%e A384245   1, 2
%e A384245   1, 1, 3
%e A384245   1, 1, 1, 4
%e A384245   1, 1, 1, 1, 5
%e A384245   1, 2, 3, 2, 1, 6
%e A384245   1, 1, 1, 1, 1, 1, 7
%e A384245   1, 2, 1, 4, 1, 2, 1, 8
%e A384245   1, 1, 1, 1, 1, 1, 1, 1, 9
%e A384245   1, 2, 1, 2, 5, 2, 1, 2, 1, 10
%t A384245 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 A384245 T[n_, k_] := Max[Intersection[infdivs[n], Divisors[k]]];
%t A384245 Table[T[n, k], {n, 1, 13}, {k, 1, n}] // Flatten
%o A384245 (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); }
%o A384245 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
%o A384245 T(n, k) = vecmax(setintersect(infdivs(n), divisors(k)));
%Y A384245 Cf. A050873, A064379, A077609, A384047, A384246 (positions of 1's).
%K A384245 nonn,tabl,easy
%O A384245 1,3
%A A384245 _Amiram Eldar_, May 23 2025