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A128671
Least number k > 0 such that k^p does not divide the denominator of generalized harmonic number H(k,p) nor the denominator of alternating generalized harmonic number H'(k,p), where p = prime(n).
3
20, 94556602, 444, 104, 77, 3504, 1107, 104, 2948, 903, 77, 1752, 77, 104, 370
OFFSET
1,1
COMMENTS
Generalized harmonic numbers are defined as H(m,k) = Sum_{i=1..m} 1/i^k. Alternating generalized harmonic numbers are defined as H'(m,k) = Sum_{i=1..m} (-1)^(i+1)*1/i^k.
a(18)..a(24) = {77,104,77,136,104,370,136}. a(26)..a(27) = {77,104}.
a(n) is currently unknown for n = {16,17,25,...}. See more details in Comments at A128672 and A125581.
LINKS
Eric Weisstein's World of Mathematics, Harmonic Number
FORMULA
a(n) = A128670(prime(n)).
EXAMPLE
a(2) = A128673(1) = 94556602.
KEYWORD
nonn,hard,more
AUTHOR
Alexander Adamchuk, Mar 24 2007, Mar 26 2007
EXTENSIONS
a(9) = 2948 and a(12) = 1752 from Max Alekseyev
Edited by Max Alekseyev, Feb 20 2019
STATUS
approved