

A175393


a(n) = number of pairs (j,k), j <= k, of divisors of 2n such that j+k divides 2n.


1



1, 2, 3, 3, 2, 7, 2, 4, 5, 5, 2, 11, 2, 4, 8, 5, 2, 12, 2, 8, 7, 4, 2, 15, 3, 4, 7, 7, 2, 20, 2, 6, 6, 4, 5, 20, 2, 4, 6, 11, 2, 17, 2, 6, 15, 4, 2, 19, 3, 8, 6, 6, 2, 17, 5, 10, 6, 4, 2, 33, 2, 4, 13, 7, 4, 15, 2, 6, 6, 12, 2, 28, 2, 4, 13, 6, 4, 15, 2, 14, 9, 4, 2, 29, 4, 4, 6, 8, 2, 38, 5, 6, 6, 4, 4
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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


CROSSREFS

Sequence in context: A319442 A299772 A304311 * A184829 A153290 A153516
Adjacent sequences: A175390 A175391 A175392 * A175394 A175395 A175396


KEYWORD

nonn


AUTHOR

Leroy Quet, Apr 29 2010


EXTENSIONS

More terms from D. S. McNeil, May 09 2010


STATUS

approved



