|
| |
|
|
A128670
|
|
Least number k>0 such that k^n does not divide the denominator of generalized harmonic number H(k,n) nor the denominator of alternating generalized harmonic number H'(k,n).
|
|
4
| |
|
|
77, 20, 94556602, 42, 444, 20, 104, 42, 76, 20, 77, 110, 3504, 20, 903, 42, 1107, 20, 104, 42, 77, 20, 2948, 110, 136, 20, 76, 42, 903, 20, 77, 42, 268, 20, 7004, 110, 1752, 20, 19203, 42, 77, 20, 104, 42, 76, 20, 370, 110, 1107, 20, 77, 42, 12246, 20, 104, 42
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,1
|
|
|
COMMENTS
| Generalized harmonic numbers are defined as H(n,k) = Sum[ 1/i^k, {i,1,n} ]. Alternating generalized harmonic numbers are defined as H'(n,k) = Sum[ (-1)^(i+1)*1/i^k, {i,1,n} ].
Some apparent periodicity in a(n) (not without exclusions): a(n) = 20 for n = 2 + 4m, a(n) = 42 for n = 4 + 12m and 8 + 12m, a(n) = 76 for n = 9 + 18m, a(n) = 77 for n = 1 + 10m, a(n) = 104 for n = 7 + 12m, a(n) = 110 for n = 12m, a(n) = 136 for n = 25 + 32m, etc.
See more details in comments for A128672 and A125581.
|
|
|
LINKS
| Max Alekseyev, Table of n, a(n) for n=1,2,...,158.
Eric Weisstein, Link to a section of The World of Mathematics. Harmonic Number.
|
|
|
CROSSREFS
| Cf. A001008, A002805, A058313, A058312, A007406, A007407, A119682,A007410, A120296, A125581, A126196, A126197, A128672, A128673, A128674, A128675, A128676, A128671, A128670.
Sequence in context: A116255 A136609 A116246 * A033397 A165943 A052202
Adjacent sequences: A128667 A128668 A128669 * A128671 A128672 A128673
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Alexander Adamchuk (alex(AT)kolmogorov.com), Mar 24 2007
|
|
|
EXTENSIONS
| More terms and b-file from Max Alekseyev (maxale(AT)gmail.com), May 07 2010
|
| |
|
|
