

A221991


a(n) is the number of terms in the expansion of (xy)(x^2y^2)*(x^3y^3)*(x^5y^5)*...*(x^p_iy^p_i), where p_i is the ith prime.


1



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


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} (1x^p_i), where p_i is the ith prime and p_0 = 1.
Offset is 1 to keep it parallel to other like sequences.


LINKS

Table of n, a(n) for n=1..51.


MATHEMATICA

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


CROSSREFS

Cf. A000124, A086781, A086795, A086796, A086817, A225549.
Sequence in context: A100433 A254343 A157006 * A279254 A212495 A083490
Adjacent sequences: A221988 A221989 A221990 * A221992 A221993 A221994


KEYWORD

nonn


AUTHOR

Robert G. Wilson v, May 12 2013


STATUS

approved



