A061002
As p runs through the primes >= 5, sequence gives { numerator of Sum_{k=1..p-1} 1/k } / p^2.
Original entry on oeis.org
1, 1, 61, 509, 8431, 39541, 36093, 375035183, 9682292227, 40030624861, 1236275063173, 6657281227331, 2690511212793403, 5006621632408586951, 73077117446662772669, 4062642402613316532391, 46571842059597941563297, 8437878094593961096374353
Offset: 3
- 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.
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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
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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)];
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Table[Function[p, Numerator[Sum[1/k, {k, p - 1}]/p^2]]@ Prime@ n, {n, 3, 20}] (* Michael De Vlieger, Feb 04 2017 *)
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a(n) = my(p=prime(n)); numerator(sum(k=1, p-1, 1/k))/p^2; \\ Michel Marcus, Dec 03 2018
A341432
a(n) is the denominator of the asymptotic density of numbers divisible by their last digit in base n.
Original entry on oeis.org
2, 2, 12, 12, 60, 20, 840, 840, 2520, 2520, 27720, 27720, 360360, 360360, 720720, 720720, 12252240, 4084080, 232792560, 77597520, 33256080, 5173168, 5354228880, 356948592, 3824449200, 26771144400, 11473347600, 80313433200, 332727080400, 2329089562800, 144403552893600
Offset: 2
For n=2, the numbers divisible by their last binary digit are the odd numbers (A005408) whose density is 1/2, therefore a(2) = 2.
For n=3, the numbers divisible by their last digit in base 3 are the numbers that are congruent to {1, 2, 4} mod 6 (A047236) whose density is 1/2, therefore a(3) = 2.
For n=10, the numbers divisible by their last digit in base 10 are A034709 whose density is 1177/2520, therefore a(10) = 2520.
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a[n_] := Denominator[Sum[GCD[k, n]/k, {k, 1, n - 1}]/n]; Array[a, 32, 2]
A120285
Numerator of harmonic number H(p-1) = Sum_{k=1..p-1} 1/k for prime p.
Original entry on oeis.org
1, 3, 25, 49, 7381, 86021, 2436559, 14274301, 19093197, 315404588903, 9304682830147, 54801925434709, 2078178381193813, 12309312989335019, 5943339269060627227, 14063600165435720745359, 254381445831833111660789
Offset: 1
- Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 22-23.
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f3:=proc(n) local p;
p:=ithprime(n);
numer(add(1/i,i=1..p-1));
end proc;
[seq(f3(n),n=1..20)];
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Numerator[Table[Sum[1/k,{k,1,Prime[n]-1}],{n,1,20}]]
Table[HarmonicNumber[p],{p,Prime[Range[20]]-1}]//Numerator (* Harvey P. Dale, May 18 2023 *)
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a(n) = my(p=prime(n)); numerator(sum(k=1, p-1, 1/k)); \\ Michel Marcus, Dec 25 2018
A076638
Denominators of harmonic numbers when the numerators are divisible by squares of primes >= 5 in the case of Wolstenholme's Theorem.
Original entry on oeis.org
12, 20, 2520, 27720, 720720, 4084080, 5173168, 80313433200, 2329089562800, 13127595717600, 485721041551200, 2844937529085600, 1345655451257488800, 3099044504245996706400, 54749786241679275146400, 3230237388259077233637600
Offset: 1
Michael Gilleland (megilleland(AT)yahoo.com), Oct 23 2002
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.
Showing 1-4 of 4 results.
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