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

1,2

Comments

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

Links

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

Eric Weisstein's World of Mathematics, Harmonic Number.

Example

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.

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}]

Crossrefs

Cf. A002805, A058312, A096304.

Sequence in context: A068585 A037472 A096304 * A158573 A194398 A047603

Adjacent sequences: A119952 A119953 A119954 * A119956 A119957 A119958

Keyword

nonn

Author

Alexander Adamchuk, Aug 02 2006

Status

approved