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

Author

Reinhard Zumkeller, Nov 28 2004

Keywords

• nonn

Examples

			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.
		

Links

• 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.

Crossrefs

Cf. A000041, A101048, A037143, A101040.

Programs

Mathematica

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