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A119955 Numbers n such that denominator of n-th Harmonic Number equals denominator of n-th Alternative Harmonic Number. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 25 02:57 EDT 2021. Contains 346282 sequences. (Running on oeis4.)