A112330 a(n) is the number of terms in the n-th row of A106394.

1, 2, 3, 3, 4, 5, 6, 5, 7, 8, 7, 6, 9, 7, 8, 8, 9, 8, 8, 9, 8, 11, 11, 11, 11, 9, 14, 10, 15, 12, 12, 15, 11, 14, 10, 14, 12, 13, 12, 16, 15, 13, 12, 12, 17, 13, 16, 16, 15, 16, 19, 14, 17, 16, 16, 21, 15, 18, 16, 18, 18, 18, 19, 21, 20, 19, 20, 22, 17, 20, 27, 19, 25, 20, 18, 23, 24

Offset: 1

Author

Leroy Quet, Sep 04 2005

Keywords

• nonn

Examples

			H(4) = 1 + 1/2 + 1/3 + 1/4 = 25/12 has the Egyptian fraction expansion, by the greedy algorithm, of 1 + 1 + 1/12. Since there are 3 terms in this expansion, a(4) = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..142

Crossrefs

Cf. A001008, A002805, A105401, A106394, A106395.

Programs

Mathematica

egyptFraction[f_] := Ceiling[1/Most[NestWhileList[# - 1/Ceiling[1/#] &, f, # != 0 &]]]; a[n_] := Length[egyptFraction[HarmonicNumber[n]]]; Array[a, 100] (* Amiram Eldar, Apr 09 2022 *)

Extensions

More terms from David Wasserman, Apr 16 2009