A076638 Denominators of harmonic numbers when the numerators are divisible by squares of primes >= 5 in the case of Wolstenholme's Theorem.

12, 20, 2520, 27720, 720720, 4084080, 5173168, 80313433200, 2329089562800, 13127595717600, 485721041551200, 2844937529085600, 1345655451257488800, 3099044504245996706400, 54749786241679275146400, 3230237388259077233637600

Offset: 1

Author

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

Keywords

• nonn
• frac

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)

Examples

			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.
		

Links

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

Crossrefs

Cf. A076637, A185399.

Programs

Mathematica

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

Extensions

More terms added by Amiram Eldar, Dec 04 2018