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A061002 As p runs through the primes >= 5, sequence gives { numerator of Sum_{k=1..p-1} 1/k } / p^2. 22
1, 1, 61, 509, 8431, 39541, 36093, 375035183, 9682292227, 40030624861, 1236275063173, 6657281227331, 2690511212793403, 5006621632408586951, 73077117446662772669, 4062642402613316532391, 46571842059597941563297, 8437878094593961096374353 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,3

COMMENTS

This is an integer by a theorem of Waring and Wolstenholme.

Conjecture: If p is the n-th prime and H(n) is the n-th harmonic number, then denominator(H(p)/H(p-1))/numerator(H(p-1)/p^2) = p^3. A193758(p)/a(n) = p^3, p > 3. - Gary Detlefs, Feb 20 2013

REFERENCES

Z. I. Borevich and I. R. Shafarevich, Number Theory. Academic Press, NY, 1966, p. 388 Problem 5.

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 115.

LINKS

Table of n, a(n) for n=3..20.

R. Mestrovic, Wolstenholme's theorem: Its Generalizations and Extensions in the last hundred and fifty years (1862-2011), arXiv:1111.3057 [math.NT], 2011.

FORMULA

a(n) = A001008(p-1)/p^2, p=A000040(n). - R. J. Mathar, Jan 09 2017

a(n) = A120285(n)/A001248(n). - R. J. Mathar, Jan 09 2017

MAPLE

A061002:=proc(n) local p;

  p:=ithprime(n);

  (1/p^2)*numer(add(1/i, i=1..p-1));

end proc;

[seq(A061002(n), n=3..20)];

MATHEMATICA

Table[Function[p, Numerator[Sum[1/k, {k, p - 1}]/p^2]]@ Prime@ n, {n, 3, 20}] (* Michael De Vlieger, Feb 04 2017 *)

CROSSREFS

Cf. A000040, A001008, A001248, A120285, A185399, A193758.

Sequence in context: A264845 A142034 A167445 * A209548 A234926 A069595

Adjacent sequences:  A060999 A061000 A061001 * A061003 A061004 A061005

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 15 2001

STATUS

approved

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Last modified August 20 17:05 EDT 2017. Contains 290836 sequences.