A119955 Numbers n such that denominator of n-th Harmonic Number equals denominator of n-th Alternative Harmonic Number.

1, 2, 3, 4, 5, 9, 10, 11, 12, 13, 14, 27, 49, 50, 51, 52, 53, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 289, 290, 291, 292, 293, 841, 842, 843, 844

Offset: 1

Author

Alexander Adamchuk, Aug 02 2006

Keywords

• nonn

Comments

Up to n=14 A002805[n] coincides with A058312[n]. a(n) up to a(12)=27 coincides with A096304[n].

Examples

			Denominators of Harmonic Number (H[n] = Sum[1/i, {i, n}]) are A002805[n] = {1,2,6,12,60,20,140,280,2520,2520,27720,27720,360360,360360,360360,...}.
Denominators of Alternative Harmonic Number (H'[n] = Sum[(-1)^(i+1)*1/i, {i, n}]) are A058312[n] = {1,2,6,12,60,60,420,840,2520,2520,27720,27720,360360,360360,72072,...}.
a(1) = 1 because A002805[1] = A058312[1].
15 is not in a(n) because A002805[15] = 360360 is not equal to A058312[15] = 72072.
		

Links

• Eric Weisstein's World of Mathematics, Harmonic Number.

Crossrefs

Cf. A002805, A058312, A096304.

Programs

Mathematica

Do[s1=Denominator[Sum[(-1)^(i+1)*1/i, {i, n}]]; s2=Denominator[Sum[1/i, {i, n}]]; If[Equal[s2, s1], Print[n]], {n, 1, 1500}]