OFFSET
2,1
COMMENTS
In an aliquot sequence, all numbers in row n can be predecessors of n. This sequence is a permutation of the composite numbers; number k appears in row A001065(k). We start with n=2 because every prime would be in row 1. Note that row 2 is empty -- as are all the rows listed in A005114. Row n contains A048138(n) numbers. When n is prime, the largest number in row n+1 is n^2. When n>7 is odd, the largest number in row n is less than ((n-1)/2)^2 and (if a strong form of the Goldbach conjecture is true) has the form pq, with primes p<q and p+q=n-1.
In row n, the first term is A070015(n), and the last term is A135244(n). - Michel Marcus, Nov 11 2014
The first row with several terms is row(6), where the difference between extreme terms is 25-6=19. The next row with a smaller difference is row(13) with a difference 35-27=8. And the next one is row(454) with a difference 602-596=6. Is there a next row with a smaller difference? - Michel Marcus, Nov 11 2014
LINKS
T. D. Noe, Rows n=2..1000 of triangle, flattened
Michel Marcus, Rows n=2..1000 of triangle, not flattened
EXAMPLE
Irregular triangle starts:
; (empty row at n=2)
4;
9;
; (empty row at n=5)
6, 25;
8;
10, 49;
15;
14;
21;
121;
27, 35;
22, 169;
16, 33;
12, 26;
39, 55;
289;
...
MAPLE
N:= 100: # for rows 2 to N, flattened
for s from 2 to N do B[s]:= NULL od:
for k from 1 to N^2 do
if not isprime(k) then
s:= numtheory:-sigma(k)-k;
if s <= N then
B[s]:= B[s], k;
fi
fi
od:
seq(B[s], s=2..N); # Robert Israel, Nov 11 2014
MATHEMATICA
nn=100; s=Table[{}, {nn}]; Do[k=DivisorSigma[1, n]-n; If[1<k<=nn, AppendTo[s[[k]], n]], {n, nn^2}]; Flatten[s]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
T. D. Noe, Dec 05 2008
STATUS
approved