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%I #15 Jun 11 2021 08:40:13
%S 20,94556602,444,104,77,3504,1107,104,2948,903,77,1752,77,104,370
%N 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).
%C 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.
%C a(18)..a(24) = {77,104,77,136,104,370,136}. a(26)..a(27) = {77,104}.
%C a(n) is currently unknown for n = {16,17,25,...}. See more details in Comments at A128672 and A125581.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>
%F a(n) = A128670(prime(n)).
%e a(2) = A128673(1) = 94556602.
%Y Cf. A128670, A001008, A002805, A058313, A058312, A007406, A007407, A119682, A007410, A120296, A125581, A126196, A126197, A128672, A128673, A128674, A128675, A128676.
%K nonn,hard,more
%O 1,1
%A _Alexander Adamchuk_, Mar 24 2007, Mar 26 2007
%E a(9) = 2948 and a(12) = 1752 from _Max Alekseyev_
%E Edited by _Max Alekseyev_, Feb 20 2019
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