A101049 Number of partitions of n into parts having at most two prime-factors.

1, 2, 3, 5, 7, 11, 15, 21, 29, 40, 53, 71, 93, 122, 158, 203, 259, 329, 415, 521, 651, 809, 1001, 1234, 1515, 1853, 2258, 2743, 3321, 4009, 4825, 5791, 6932, 8277, 9859, 11715, 13889, 16431, 19398, 22854, 26873, 31539, 36949, 43210, 50446, 58796, 68419

Offset

1,2

Links

Table of n, a(n) for n=1..47.

Feihu Liu, Guoce Xin, and Chen Zhang, Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS, arXiv:2412.18744 [math.CO], 2024. See p. 15.

Example

n=10 has two partitions with parts having more than two
prime-factors: 10 = 2*2*2 + 2 = 2*2*2 + 1 + 1, therefore
a(10) = A000041(10) - 2 = 42 - 2 = 40.

Mathematica

Table[Count[IntegerPartitions[n], _?(AllTrue[#, PrimeOmega[#] <= 2 &] &)], {n, 40}] (* Michael De Vlieger, Jan 14 2025 *)

Crossrefs

Cf. A000041, A101048, A037143, A101040.

Sequence in context: A332638 A035977 A288256 * A333193 A035986 A035996

Adjacent sequences: A101046 A101047 A101048 * A101050 A101051 A101052

Keyword

nonn

Author

Reinhard Zumkeller, Nov 28 2004

Status

approved