cp's OEIS Frontend

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.

%I A137510 #24 May 19 2019 02:00:09
%S A137510 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,
%T A137510 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,
%U A137510 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
%N 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.
%C A137510 The length of row n is A264440(n). - _Wolfdieter Lang_, Jan 16 2016
%C A137510 Row n lists the nontrivial divisors of n, or 0 if there are no such divisors. - _Omar E. Pol_, Nov 22 2010
%e A137510 From _Omar E. Pol_, Nov 22 2010: (Start)
%e A137510 The irregular triangle begins:
%e A137510 0;
%e A137510 0;
%e A137510 0;
%e A137510 2;
%e A137510 0;
%e A137510 2, 3;
%e A137510 0;
%e A137510 2, 4;
%e A137510 3;
%e A137510 2, 5;
%e A137510 0,
%e A137510 2, 3, 4, 6;
%e A137510 (End)
%p A137510 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
%p A137510 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
%t A137510 Array[Complement[Divisors@ #, {1, #}] &, {42}] /. {} -> {0} // Flatten (* _Michael De Vlieger_, Jan 16 2016 *)
%Y A137510 Cf. A070824, A027750, A027751, A264440 (row length). Row sums give A048050.
%K A137510 nonn,tabf,easy
%O A137510 1,4
%A A137510 _N. J. A. Sloane_, May 08 2008
%E A137510 More terms from _R. J. Mathar_ and _Emeric Deutsch_, May 23 2008