A168173 Number of partitions of n in which the sum of reciprocals of parts is less than 1.

0, 1, 1, 1, 2, 3, 3, 4, 4, 6, 8, 12, 13, 16, 18, 21, 25, 32, 38, 46, 55, 65, 78, 92, 103, 122, 140, 165, 193, 229, 264, 305, 345, 395, 451, 517, 590, 682, 781, 893, 1013, 1165, 1324, 1518, 1717, 1945, 2188, 2468, 2753, 3089, 3457, 3865, 4321, 4856, 5441, 6108, 6831

Offset

1,5

Links

Table of n, a(n) for n=1..57.

Maple

a := proc (n) local P, ct, j: with(combinat): P := partition(n): ct := 0: for j to numbpart(n) do if add(1/P[j][i], i = 1 .. nops(P[j])) < 1 then ct := ct+1 else end if end do: ct end proc: seq(a(n), n = 1 .. 60); # Emeric Deutsch, Dec 02 2009

Mathematica

Table[Count[IntegerPartitions[n], _?(Total[1/#]<1&)], {n, 60}] (* Harvey P. Dale, Dec 14 2012 *)

Crossrefs

Cf. A051908.

Sequence in context: A267597 A238221 A320052 * A095916 A130121 A007898

Adjacent sequences: A168170 A168171 A168172 * A168174 A168175 A168176

Keyword

nonn

Author

Vladeta Jovovic, Nov 19 2009

Extensions

Extended by Emeric Deutsch, Dec 02 2009

Status

approved