OFFSET
1,2
COMMENTS
The sum of any two divisors of an odd number n never divides n.
From Robert Israel, Oct 09 2017: (Start)
(1,1) and (n,n) are always such pairs, so a(n) >= 2 for n >= 2.
a(n)=2 if and only if n is a prime other than 3.
a(3^k) = 2*k+1.
a(p^k) = k+1 for primes other than 3. (End)
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
The divisors of 2*6 = 12 are 1,2,3,4,6,12. The pairs of these divisors that each sum to a divisor of 12 are 1+1 = 2, 1+2 = 3, 1+3 = 4, 2+2 = 4, 2+4 = 6, 3+3 = 6, and 6+6 = 12. There are seven of these pairs, so a(6) = 7.
MAPLE
f:= proc(n) local D, k, t;
D:= numtheory:-divisors(2*n);
t:= 0;
for k from 1 to nops(D) do
t:= t + nops(select(j -> 2*n mod (D[j]+D[k])=0, [$1..k]))
od;
t
end proc:
map(f, [$1..100]); # Robert Israel, Oct 09 2017
MATHEMATICA
Table[Length[Select[Total/@Union[Sort/@Tuples[Divisors[2 n], 2]], Mod[2 n, #]==0&]], {n, 100}] (* Harvey P. Dale, Apr 09 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Leroy Quet, Apr 29 2010
EXTENSIONS
More terms from D. S. McNeil, May 09 2010
STATUS
approved