A278048 -id:A278048 - cp's OEIS frontend

A278047 Let v = list of denominators of Farey series of order n (see A006843); let b(n) = Sum 1/(kk'(k+k')), where (k,k') are pairs of successive terms of v; a(n) = numerator of b(n).

1, 1, 7, 4, 37, 53, 707, 85, 179077, 289613, 379721, 641671, 62836087, 35819033, 6367281023, 55181728027, 13442946373, 490167893, 596530310479, 576997238399, 116144361532321, 4931206160615, 164890340129357, 1514840590670747, 10181612956306486603, 3295813969039399097

Offset: 1

N. J. A. Sloane, Nov 22 2016

			The fractions b(n) are 1/2, 1/3, 7/30, 4/21, 37/252, 53/396, 707/6435, 85/858, 179077/2042040, 289613/3527160, 379721/5290740, 641671/9360540, 62836087/1029659400, 35819033/617795640, ...

J. Lehner and M. Newman, Sums involving Farey fractions, Acta Arithmetica 15.2 (1969): 181-187.

Cf. A006843, A005728, A240877, A278046, A278048.

Farey := proc(n) sort(convert(`union`({0}, {seq(seq(m/k, m=1..k), k=1..n)}), list)) end:
ans:=[];
for n from 1 to 50 do
t1:=denom(Farey(n));
t2:=add( 1/(t1[i]*t1[i+1]*(t1[i]+t1[i+1])),i=1..nops(t1)-1);
ans:=[op(ans),t2];
od:
ans;
map(numer,ans); # A278047
map(denom,ans); # A278048

cp's OEIS Frontend

A278047 Let v = list of denominators of Farey series of order n (see A006843); let b(n) = Sum 1/(kk'(k+k')), where (k,k') are pairs of successive terms of v; a(n) = numerator of b(n).

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cp's OEIS Frontend

A278047 Let v = list of denominators of Farey series of order n (see A006843); let b(n) = Sum 1/(k*k'*(k+k')), where (k,k') are pairs of successive terms of v; a(n) = numerator of b(n).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

A278047 Let v = list of denominators of Farey series of order n (see A006843); let b(n) = Sum 1/(kk'(k+k')), where (k,k') are pairs of successive terms of v; a(n) = numerator of b(n).