This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A101049 #6 Jan 14 2025 11:06:47
%S A101049 1,2,3,5,7,11,15,21,29,40,53,71,93,122,158,203,259,329,415,521,651,
%T A101049 809,1001,1234,1515,1853,2258,2743,3321,4009,4825,5791,6932,8277,9859,
%U A101049 11715,13889,16431,19398,22854,26873,31539,36949,43210,50446,58796,68419
%N A101049 Number of partitions of n into parts having at most two prime-factors.
%H A101049 Feihu Liu, Guoce Xin, and Chen Zhang, <a href="https://arxiv.org/abs/2412.18744">Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS</a>, arXiv:2412.18744 [math.CO], 2024. See p. 15.
%e A101049 n=10 has two partitions with parts having more than two
%e A101049 prime-factors: 10 = 2*2*2 + 2 = 2*2*2 + 1 + 1, therefore
%e A101049 a(10) = A000041(10) - 2 = 42 - 2 = 40.
%t A101049 Table[Count[IntegerPartitions[n], _?(AllTrue[#, PrimeOmega[#] <= 2 &] &)], {n, 40}] (* _Michael De Vlieger_, Jan 14 2025 *)
%Y A101049 Cf. A000041, A101048, A037143, A101040.
%K A101049 nonn
%O A101049 1,2
%A A101049 _Reinhard Zumkeller_, Nov 28 2004