A121594 Numbers k such that k does not divide the denominator of the k-th alternating Harmonic number.

15, 28, 75, 77, 104, 187, 196, 203, 210, 222, 228, 235, 238, 328, 345, 375, 551, 620, 847, 888, 1036, 1107, 1204, 1349, 1352, 1372, 1391, 1430, 1457, 1469, 1470, 1498, 1666, 1687, 1855, 1875, 2133, 2301, 2425, 2440, 2556, 2678, 2948, 3179, 3337, 3477

Offset

1,1

Comments

Indices k such that A119788(k) is not equal to 1.

Also indices k such that numerators of k*H'(k) = A119787(k) and H'(k) = A058313(k) are different (H'(k) is the alternating harmonic number H'(k) = Sum_{j=1..k} (-1)^(j+1)*1/j). The ratio of numerators A119787(k)/A058313(k) for k = 1..400 is given in A119788(k). A121595(k) = A119788(a(k)) is the compressed version of A119788(k) (all 1 entries are excluded).

Links

Giovanni Resta, Table of n, a(n) for n = 1..900

Mathematica

Do[H=Sum[(-1)^(i+1)*1/i, {i, 1, n}]; a=Numerator[n*H]; b=Numerator[H]; If[ !Equal[a, b], Print[{n, a/b}]], {n, 1, 6000}]
f=0; Do[f=f+(-1)^(n+1)/n; If[ !IntegerQ[Denominator[f]/n], Print[n]], {n, 1, 100}] (* Alexander Adamchuk, Jan 02 2007 *)

Crossrefs

Cf. A119788, A119787, A058313, A121595.

Cf. A058312 = Denominator of the n-th alternating harmonic number, Sum_{k=1..n} (-1)^(k+1)/k. A074791 = numbers k such that k does not divide the denominator of the k-th Harmonic number.

Sequence in context: A357278 A343067 A223442 * A163286 A022997 A256876

Adjacent sequences: A121591 A121592 A121593 * A121595 A121596 A121597

Keyword

nonn

Author

Alexander Adamchuk, Aug 09 2006

Status

approved