OFFSET
1,13
FORMULA
a(n) = Sum_{i=1..floor((n-1)/2)} [d(i) = d(n-i)], where [] is the Iverson bracket and d is the number of divisors of n (A000005).
EXAMPLE
a(16) = 3; There are 3 ways to write 16 as the sum of 2 distinct numbers with the same number of divisors: 16 = 13+3 (13 and 3 both have 2 divisors), 16 = 11+5 (11 and 5 both have 2 divisors), 16 = 10+6 (10 and 6 both have 4 divisors).
MATHEMATICA
Table[Sum[KroneckerDelta[DivisorSigma[0, i], DivisorSigma[0, n - i]], {i, Floor[(n - 1)/2]}], {n, 100}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Apr 02 2020
STATUS
approved