A355860 Triangle read by rows: T(n,k) = n*k/(n + k) if n+k divides n*k, otherwise T(n,k) = 0; n >= 1, k >= 1.

0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 4, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7

Offset: 1

Author

Ctibor O. Zizka, Jul 19 2022

Keywords

• nonn
• tabl

Examples

			The triangle begins:
  0;
  0, 1;
  0, 0, 0;
  0, 0, 0, 2;
  0, 0, 0, 0, 0;
  0, 0, 2, 0, 0, 3;
and so on.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..22155; the first 210 rows of the triangle

Crossrefs

Cf. also A106448.

Programs

Mathematica

T[n_, k_] := If[Divisible[n*k, n + k], n*k/(n + k), 0]; Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Amiram Eldar, Jul 20 2022 *)

PARI

up_to = 105;
A355860tr(n,k) = ((q->if(1==denominator(q),q,0))((n*k)/(n+k)));
A355860list(up_to) = { my(v = vector(up_to), i=0); for(n=1,oo, for(k=1,n, if(i++ > up_to, return(v)); v[i] = A355860tr(n,k))); (v); };
v355860 = A355860list(up_to);
A355860(n) = v355860[n]; \\ Antti Karttunen, Jan 16 2025

Extensions

Data section extended up to a(105) by Antti Karttunen, Jan 16 2025