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A168173 Number of partitions of n in which the sum of reciprocals of parts is less than 1. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 6 23:12 EST 2023. Contains 360111 sequences. (Running on oeis4.)