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

Author

Vladeta Jovovic, Nov 19 2009

Keywords

• nonn

Crossrefs

Cf. A051908.

Programs

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 *)

Extensions

Extended by Emeric Deutsch, Dec 02 2009