A280634 - OEIS

%I #15 Jul 27 2019 02:09:24

%S 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,

%T 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,

%U 1,5,0,7,1,3,1,3,2,3,1,5,0,6,0,7,1,3,1,5,0,3

%N Number of partitions of 2n into two refactorable parts.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RefactorableNumber.html">Refactorable Number</a>

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F 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.

%e a(5) = 2; There are two partitions of 2*5 = 10 into two refactorable parts: (1,9) and (2,8).

%p 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);

%t 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 *)

%Y Cf. A000005, A033950, A172398, A280226.

%K nonn,easy

%O 1,5

%A _Wesley Ivan Hurt_, Jan 06 2017