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A076638 Denominators of harmonic numbers when the numerators are divisible by squares of primes >= 5 in the case of Wolstenholme's Theorem. 1
12, 20, 2520, 27720, 720720, 4084080, 5173168, 80313433200, 2329089562800, 13127595717600, 485721041551200, 2844937529085600, 1345655451257488800, 3099044504245996706400, 54749786241679275146400, 3230237388259077233637600 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

From Bernard Schott, Dec 28 2018: (Start)

By Wolstenholme's Theorem, if p prime >= 5, the numerator of the harmonic number H_{p-1} is always divisible by p^2. The obtained quotients are in A061002.

The numerators of H_7 and H_{29} are also divisible by prime squares, respectively by 11^2 and 43^2, but not in the case of Wolstenholme's theorem, so the denominators of H_7 and H_{29} are not in this sequence here. (End)

LINKS

Table of n, a(n) for n=1..16.

Eric Weisstein's World of Mathematics, Wolstenholme's Theorem

EXAMPLE

a(1)=12 because the numerator of H_4 = 25/12 is divisible by the square of 5;

a(2)=20 because the numerator of H_6 = 49/20 is divisible by the square of 7.

MATHEMATICA

a[p_] := Denominator[HarmonicNumber[p - 1]]; a /@ Prime@Range[3, 20] (* Amiram Eldar, Dec 28 2018 *)

CROSSREFS

Cf. A076637, A185399.

Sequence in context: A231400 A231467 A078600 * A129939 A082799 A089320

Adjacent sequences:  A076635 A076636 A076637 * A076639 A076640 A076641

KEYWORD

nonn,frac

AUTHOR

Michael Gilleland (megilleland(AT)yahoo.com), Oct 23 2002

EXTENSIONS

More terms added by Amiram Eldar, Dec 04 2018

STATUS

approved

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Last modified May 10 22:16 EDT 2021. Contains 343780 sequences. (Running on oeis4.)