A317443 a(n) = number of k with 1 <= k <= n-1 such that a(k) + a(n-k) is not squarefree.

0, 1, 0, 2, 0, 3, 0, 7, 0, 7, 0, 10, 0, 9, 2, 8, 4, 9, 8, 10, 8, 11, 10, 17, 8, 13, 12, 15, 4, 19, 4, 25, 6, 17, 8, 25, 12, 19, 10, 27, 10, 23, 14, 22, 16, 25, 16, 26, 12, 21, 16, 22, 14, 31, 16, 40, 14, 29, 20, 32, 14, 27, 22, 35, 24, 33, 24, 32, 28, 25, 18

Offset: 1

Author

Rémy Sigrist, Jul 28 2018

Keywords

• nonn

Comments

We consider that 0 is not squarefree.

The scatterplot of the sequence has stripes linked to the 2-adic valuation of n.

See A317420 for similar sequences.

Examples

			For n = 4:
- a(1) + a(3) = 0 + 0 = 0 is not squarefree,
- a(2) + a(2) = 1 + 1 = 2 is squarefree,
- a(3) + a(1) = 0 + 0 = 0 is not squarefree,
- hence a(4) = 2.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, Colored scatterplot of the first 1000000 terms (where the color is function of A007814(n))

Crossrefs

Cf. A007814, A013929, A317420.

Programs

PARI

a = vector(71); for (n=1, #a, a[n] = sum(k=1, n-1, !issquarefree(a[k]+a[n-k])); print1 (a[n] ", "))