A128670 - OEIS

%I #15 Feb 16 2025 08:33:05

%S 77,20,94556602,42,444,20,104,42,76,20,77,110,3504,20,903,42,1107,20,

%T 104,42,77,20,2948,110,136,20,76,42,903,20,77,42,268,20,7004,110,1752,

%U 20,19203,42,77,20,104,42,76,20,370,110,1107,20,77,42,12246,20,104,42

%N 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).

%C Generalized harmonic numbers are defined as H(m,k) = Sum_{j=1..m}1/j^k. Alternating generalized harmonic numbers are defined as H'(m,k) = Sum_{j=1..m} (-1)^(j+1)/j^k.

%C Some apparent periodicity in {a(n)} (not without exceptions): 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.

%C See more details in Comments at A128672 and A125581.

%H Max Alekseyev, <a href="/A128670/b128670.txt">Table of n, a(n) for n=1..158</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HarmonicNumber.html">Harmonic Number</a>

%Y Cf. A001008, A002805, A058313, A058312, A007406, A007407, A119682, A007410, A120296, A125581, A126196, A126197, A128672, A128673, A128674, A128675, A128676, A128671, A128670.

%K nonn,changed

%O 1,1

%A _Alexander Adamchuk_, Mar 24 2007

%E More terms and b-file from _Max Alekseyev_, May 07 2010