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 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; text; internal format)
 OFFSET 1,1 COMMENTS 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. 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. See more details in Comments at A128672 and A125581. LINKS Max Alekseyev, Table of n, a(n) for n=1..158. Eric Weisstein's 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 * A225522 A033397 A260023 Adjacent sequences:  A128667 A128668 A128669 * A128671 A128672 A128673 KEYWORD nonn AUTHOR Alexander Adamchuk, Mar 24 2007 EXTENSIONS More terms and b-file from Max Alekseyev, May 07 2010 STATUS approved

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Last modified September 25 10:45 EDT 2022. Contains 356978 sequences. (Running on oeis4.)