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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. 25
 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 The sequence which gives the numerators of H_{p-1} = Sum_{k=1..p-1} 1/k } for p prime >= 5 is A076637. - Bernard Schott, Dec 02 2018 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 Muniru A Asiru, Table of n, a(n) for n = 3..340 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 *) PROG (GAP) List(List(Filtered([5..80], p->IsPrime(p)), i->Sum([1..i-1], k->1/k)/i^2), NumeratorRat); # Muniru A Asiru, Dec 02 2018 (PARI) a(n) = my(p=prime(n)); numerator(sum(k=1, p-1, 1/k))/p^2; \\ Michel Marcus, Dec 03 2018 CROSSREFS Cf. A000040, A001008, A001248, A120285, A185399, A193758. Sequence in context: A142034 A167445 A302531 * A303412 A209548 A302898 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 February 21 02:02 EST 2020. Contains 332086 sequences. (Running on oeis4.)