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

1,4

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

Links

Table of n, a(n) for n=1..97.

Example

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)

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 *)

Crossrefs

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

Sequence in context: A299761 A141099 A127710 * A247303 A067871 A198632

Adjacent sequences: A137507 A137508 A137509 * A137511 A137512 A137513

Keyword

nonn,tabf,easy

Author

N. J. A. Sloane, May 08 2008

Extensions

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

Status

approved