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A355248
Number of ways to write n as the sum of (exactly) 3 positive integers with the same number of divisors.
0
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
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
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 25 2022
STATUS
approved