A335060 -id:A335060 - cp's OEIS frontend

A339388 a(n) is the number of k in the range 1..n-1 such that a(k)*a(n-k) <= a(n-1).

0, 1, 2, 3, 4, 5, 4, 2, 2, 4, 6, 8, 10, 8, 4, 3, 2, 2, 4, 6, 8, 10, 10, 12, 10, 6, 4, 2, 2, 4, 6, 8, 14, 17, 20, 17, 14, 10, 6, 2, 2, 4, 6, 10, 16, 20, 26, 24, 20, 14, 10, 2, 2, 4, 6, 11, 16, 21, 26, 27, 24, 20, 14, 6, 2, 2, 4, 8, 16, 22, 28, 34, 36, 34, 20

Offset: 1

Rémy Sigrist, Dec 02 2020

nonn

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Density plot of the first 1000000 terms

Cf. A335060, A339389.

{ for (n=1, #a=vector(75), print1 (a[n] = sum(k=1, n-1, a[k]*a[n-k]<=a[n-1]) ", ")) }

A335190 a(n) is the number of values of k < n for which 4*(a(k) + a(n-k)) <= n.

Original entry on oeis.org

0, 1, 0, 2, 2, 1, 2, 6, 2, 4, 0, 5, 4, 2, 6, 8, 4, 7, 2, 8, 6, 3, 10, 12, 6, 10, 4, 11, 8, 4, 12, 14, 8, 13, 6, 14, 10, 5, 14, 18, 10, 14, 8, 17, 10, 10, 18, 20, 14, 17, 12, 20, 10, 13, 16, 22, 16, 14, 14, 25, 10, 14, 16, 24, 22, 19, 16, 28, 12, 17, 20, 30, 24

Offset: 1

Rémy Sigrist, May 26 2020

This sequence is a variant of A335060.

Graphically, we have an overlay of four curves that correspond to the quadrisections of the sequence.

			The first terms, alongside the corresponding k's, are:
  n   a(n)  k's
  --  ----  ---------------------
   1     0  {}
   2     1  {1}
   3     0  {}
   4     2  {1, 3}
   5     2  {2, 3}
   6     1  {3}
   7     2  {1, 6}
   8     6  {1, 2, 3, 5, 6, 7}
   9     2  {3, 6}
  10     4  {1, 3, 7, 9}
  11     0  {}
  12     5  {1, 3, 6, 9, 11}

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Colored scatterplot of the first 100000 terms

Cf. A335060.

for (n=1, #a=vector(73), print1 (a[n]=sum(k=1, n-1, a[k]+a[n-k]<=n/4)", "))

cp's OEIS Frontend

A339388 a(n) is the number of k in the range 1..n-1 such that a(k)*a(n-k) <= a(n-1).

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