A382954 Number of ways to partition distinct prime numbers into three disjoint sets such that the sum of each set equals n.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 1, 3, 2, 8, 1, 1, 4, 0, 14, 9, 1, 4, 7, 16, 26, 31, 17, 3, 19, 39, 54, 20, 62, 9, 41, 96, 89, 62, 66, 34, 59, 197, 241, 289, 69, 124, 184, 133, 481, 440, 148, 225, 394, 709, 808, 984, 555, 414, 799

Offset

0,25

Comments

Conjecture: a(n) > 0 for n > 35.

Links

Table of n, a(n) for n=0..76.

Formula

a(n) = 1/6 * [(x*y*z)^n] Product_{p prime} (1 + x^p + y^p + z^p) for n > 0.

Example

a(29) = 3: [29; 19, 7, 3; 13, 11, 5], [29; 17, 7, 3, 2; 13, 11, 5], [29; 17, 7, 5; 13, 11, 3, 2].
a(30) = 2: [23, 7; 19, 11; 17, 13], [23, 5, 2; 19, 11; 17, 13].

Crossrefs

Cf. A000607, A258281, A382871.

Sequence in context: A185370 A384765 A352747 * A364955 A112517 A112519

Adjacent sequences: A382951 A382952 A382953 * A382955 A382956 A382957

Keyword

nonn

Author

Seiichi Manyama, Apr 10 2025

Status

approved