OFFSET
1,8
COMMENTS
LINKS
Eric Weisstein's World of Mathematics, Abundance
Eric Weisstein's World of Mathematics, Quasiperfect Number
FORMULA
T(n,1) = -1; T(n,k) = A196020(n,k), for k >= 2.
EXAMPLE
Triangle begins:
-1;
-1;
-1, 1;
-1, 0;
-1, 3;
-1, 0, 1;
-1, 5, 0;
-1, 0, 0;
-1, 7, 3;
-1, 0, 0, 1;
-1, 9, 0, 0;
-1, 0, 5, 0;
-1, 11, 0, 0;
-1, 0, 0, 3;
-1, 13, 7, 0, 1;
-1, 0, 0, 0, 0;
-1, 15, 0, 0, 0;
-1, 0, 9, 5, 0;
-1, 17, 0, 0, 0;
-1, 0, 0, 0, 3;
-1, 19, 11, 0, 0, 1;
-1, 0, 0, 7, 0, 0;
-1, 21, 0, 0, 0, 0;
-1, 0, 13, 0, 0, 0;
...
For n = 15 the divisors of 15 are 1, 3, 5, 15 hence the abundance of 15 is 1 + 3 + 5 + 15 - 2*15 = 1 + 3 + 5 - 15 = -6. On the other hand the 15th row of triangle is -1, 13, 7, 0, 1, hence the alternating row sum is -1 - 13 + 7 - 0 + 1 = -6, equalling the abundance of 15.
If n is even then the alternating sum of the n-th row of triangle is simpler than the sum of divisors of n minus 2*n. Example: the sum of divisors of 24 minus 2*24 is 1 + 2 + 3 + 4 + 6 + 8 + 12 + 24 - 2*24 = 60 - 48 = 12, and the alternating sum of the 24th row of triangle is -1 - 0 + 13 - 0 + 0 - 0 = 12.
CROSSREFS
KEYWORD
sign,tabf,nice
AUTHOR
Omar E. Pol, Dec 26 2013
STATUS
approved