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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Generalized harmonic numbers are defined as H(n,k) = Sum_{i=1..n} 1/i^k. Alternating generalized harmonic numbers are defined as H'(n,k) = Sum_{i=1..n} (-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 for A128672 and A125581.

LINKS

Table of n, a(n) for n=1..15.

Eric Weisstein's World of Mathematics, Harmonic Number

FORMULA

a(n) = A128670( Prime(n) ).

EXAMPLE

a(2) = A128673(1) = 94556602.

CROSSREFS

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

Sequence in context: A180725 A013812 A013894 * A172766 A048948 A172834

Adjacent sequences:  A128668 A128669 A128670 * A128672 A128673 A128674

KEYWORD

hard,more,nonn

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

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Last modified November 16 20:04 EST 2019. Contains 329201 sequences. (Running on oeis4.)