A221991 a(n) is the number of terms in the expansion of (x-y)(x^2-y^2)*(x^3-y^3)*(x^5-y^5)*...*(x^p_i-y^p_i), where p_i is the i-th prime.

2, 4, 6, 8, 10, 20, 22, 36, 42, 66, 90, 110, 142, 184, 232, 284, 342, 400, 458, 532, 604, 678, 756, 838, 928, 1026, 1126, 1230, 1336, 1446, 1558, 1686, 1816, 1954, 2092, 2242, 2392, 2550, 2712, 2880, 3052, 3232, 3412, 3604, 3796, 3994, 4192, 4404, 4626, 4854, 5082

Offset: 1

Author

Robert G. Wilson v, May 12 2013

Keywords

• nonn

Comments

In the definition one can take y=1. Thus the sequence becomes the number of terms in the polynomial of the product{k=0..n} (1-x^p_i), where p_i is the i-th prime and p_0 = 1.

Offset is 1 to keep it parallel to other like sequences.

Crossrefs

Cf. A000124, A086781, A086795, A086796, A086817, A225549.

Programs

Mathematica

f[n_] := Length@ ExpandAll[(1 - x) Product[(1 - x^Prime[k]), {k, n}]]; Array[f, 51, 0]