A220489 Total number of smallest parts in all partitions of n minus the total number of smallest parts that are also emergent parts in all partitions of n with at least one distinct part.

1, 3, 5, 10, 14, 26, 34, 56, 77, 114, 153, 227, 296, 414, 555, 750, 981, 1316, 1702, 2241, 2887, 3727, 4761, 6112, 7725, 9787, 12316, 15473, 19307, 24099, 29867, 37004, 45626, 56147, 68856, 84297, 102793, 125167, 151969, 184166, 222553, 268529, 323152

Offset: 1

Author

Omar E. Pol, Feb 24 2013

Keywords

• nonn

Comments

First differs from A092269 at a(7).

For the definition of "emergent part" see A182699, A182709.

Crossrefs

Cf. A000005, A000041, A000070, A000203, A002865, A092269, A120452, A195820, A220479, A220483.

Formula

a(n) = spt(n) - A220483(n) = 1 + sigma(n) + A000070(n) - p(n-1) - d(n) - n.

a(n) = A092269(n) - A220483(n) = 1 + A000203(n) + A000070(n) - A000041(n-1) - A000005(n) - n.