A137510 Irregular triangle read by rows in which row n lists the divisors of n in the range 1 < d < n; or 0 if there are no such divisors.

0, 0, 0, 2, 0, 2, 3, 0, 2, 4, 3, 2, 5, 0, 2, 3, 4, 6, 0, 2, 7, 3, 5, 2, 4, 8, 0, 2, 3, 6, 9, 0, 2, 4, 5, 10, 3, 7, 2, 11, 0, 2, 3, 4, 6, 8, 12, 5, 2, 13, 3, 9, 2, 4, 7, 14, 0, 2, 3, 5, 6, 10, 15, 0, 2, 4, 8, 16, 3, 11, 2, 17, 5, 7, 2, 3, 4, 6, 9, 12, 18, 0, 2, 19, 3, 13, 2, 4, 5, 8, 10, 20, 0, 2, 3, 6, 7

Offset: 1

Author

N. J. A. Sloane, May 08 2008

Keywords

• nonn
• tabf
• easy

Comments

The length of row n is A264440(n). - Wolfdieter Lang, Jan 16 2016

Row n lists the nontrivial divisors of n, or 0 if there are no such divisors. - Omar E. Pol, Nov 22 2010

Examples

			From _Omar E. Pol_, Nov 22 2010: (Start)
The irregular triangle begins:
0;
0;
0;
2;
0;
2, 3;
0;
2, 4;
3;
2, 5;
0,
2, 3, 4, 6;
(End)
		

Crossrefs

Cf. A070824, A027750, A027751, A264440 (row length). Row sums give A048050.

Programs

Maple

for n from 1 to 80 do if isprime(n) or n = 1 then printf("0,") ; else dvs := sort(convert(numtheory[divisors](n) minus {1,n},list) ) ; for d in dvs do printf("%d,",d) ; od: fi ; od: # R. J. Mathar, May 23 2008
with(numtheory): A:=proc (n) local div: div:=divisors(n): `minus`(div, {div[tau(n)], div[1]}) end proc: for n to 35 do A(n) end do: a:=proc (n) if A(n)={} then 0 else seq(A(n)[j],j=1..tau(n)-2) end if end proc: for n to 35 do a(n) end do; # yields sequence in triangular form - Emeric Deutsch, May 25 2008

Mathematica

Array[Complement[Divisors@ #, {1, #}] &, {42}] /. {} -> {0} // Flatten (* Michael De Vlieger, Jan 16 2016 *)

Extensions

More terms from R. J. Mathar and Emeric Deutsch, May 23 2008