A355248 Number of ways to write n as the sum of (exactly) 3 positive integers with the same number of divisors.

0, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 2, 3, 2, 1, 3, 2, 5, 3, 3, 3, 5, 5, 5, 5, 5, 6, 9, 5, 8, 5, 8, 4, 12, 5, 11, 8, 12, 10, 13, 5, 14, 10, 16, 9, 17, 8, 19, 10, 19, 15, 24, 12, 22, 14, 24, 16, 27, 16, 25, 13, 23, 22, 33, 15, 29, 17, 35, 22, 37, 17, 37, 15, 32, 28, 44, 27, 41, 26, 40

Offset

0,10

Links

Table of n, a(n) for n=0..79.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} [d(j) = d(i) = d(n-i-j)], where d(n) is the number of divisors of n and [ ] is the (generalized) Iverson bracket.

Example

a(17) = 5; there are 5 ways to write 17 as the sum of 3 positive integers with the same number of divisors: 2+2+13 = 3+3+11 = 3+7+7 = 4+4+9 = 5+5+7.

Crossrefs

Cf. A000005.

Sequence in context: A198325 A293909 A002850 * A111944 A109814 A133088

Adjacent sequences: A355245 A355246 A355247 * A355249 A355250 A355251

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 25 2022

Status

approved