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

1,4

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.

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))

Example

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.

Prog

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

Crossrefs

Cf. A007814, A013929, A317420.

Sequence in context: A331176 A076563 A163974 * A308218 A067165 A079981

Adjacent sequences: A317440 A317441 A317442 * A317444 A317445 A317446

Keyword

nonn

Author

Rémy Sigrist, Jul 28 2018

Status

approved