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

1,2

Comments

First differs from A092269 at a(7).

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

Links

Table of n, a(n) for n=1..43.

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.

Crossrefs

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

Sequence in context: A137630 A320886 A323433 * A229915 A092269 A323429

Adjacent sequences: A220486 A220487 A220488 * A220490 A220491 A220492

Keyword

nonn

Author

Omar E. Pol, Feb 24 2013

Status

approved