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A280634
Number of partitions of 2n into two refactorable parts.
3
1, 1, 0, 0, 2, 0, 1, 1, 1, 2, 0, 1, 2, 0, 1, 1, 0, 2, 1, 0, 2, 1, 0, 3, 0, 1, 1, 0, 2, 1, 1, 2, 0, 2, 0, 2, 2, 1, 1, 3, 1, 2, 1, 1, 2, 3, 0, 5, 2, 2, 1, 2, 2, 3, 1, 4, 1, 4, 0, 5, 1, 2, 1, 3, 1, 3, 1, 3, 1, 5, 0, 7, 1, 3, 1, 3, 2, 3, 1, 5, 0, 6, 0, 7, 1, 3, 1, 5, 0, 3
OFFSET
1,5
FORMULA
a(n) = Sum_{i=1..n} (1-sign(i mod d(i))) * (1-sign((2n-i) mod d(2n-i))) where d(n) is the number of divisors of n.
EXAMPLE
a(5) = 2; There are two partitions of 2*5 = 10 into two refactorable parts: (1,9) and (2,8).
MAPLE
with(numtheory): A280634:=n->add((1-signum((i mod tau(i))))*(1-signum((2*n-i) mod tau(2*n-i))), i=1..n): seq(A280634(n), n=1..150);
MATHEMATICA
Table[Sum[(1 - Sign[Mod[i, DivisorSigma[0, i]]]) (1 - Sign[Mod[#, DivisorSigma[0, #]]] &[2 n - i]), {i, n}], {n, 90}] (* Michael De Vlieger, Jan 07 2017 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wesley Ivan Hurt, Jan 06 2017
STATUS
approved