A175313 Number of distinct sums of pairs of reciprocals of 1,2,3,...,n.

1, 3, 6, 10, 15, 19, 26, 34, 43, 53, 64, 72, 85, 99, 111, 127, 144, 160, 179, 195, 215, 237, 260, 279, 304, 330, 357, 382, 411, 432, 463, 495, 528, 562, 594, 623, 660, 698, 737, 769, 810, 846, 889, 932, 969, 1015, 1062, 1104, 1153, 1203, 1254, 1305, 1358, 1410

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Example

For n=3, we have the reciprocals {1, 1/2, 1/3} with sums of pairs {1+1, 1+1/2, 1+1/3, 1/2+1/2, 1/2+1/3, 1/3+1/3} = {2, 3/2, 4/3, 1, 5/6, 2/3}. These are all distinct, so a(3) = 6.

Maple

N:= 1000;
S:= {}:
for n from 1 to N do
  S:= S union {seq(1/n + 1/j, j=1..n)};
  A[n]:= nops(S);
od:
seq(A[n], n=1..N);
# Robert Israel, Jul 09 2014

Mathematica

M = 100; S = {};
For[n = 1, n <= M, n++, S = S ~Union~ Table[1/n + 1/j, {j, 1, n}]; A[n] = Length[S]];
Array[A, M] (* Jean-François Alcover, Mar 22 2019, from Maple *)

Prog

(PARI) a(n) = {vr = vector(n, i, 1/i); vds = []; for (i=1, n, for (j=1, i, vds = Set(concat(vds, vr[i]+vr[j])); ); ); #vds; } \\ Michel Marcus, Jul 09 2014

Crossrefs

Sequence in context: A310075 A347275 A233774 * A289387 A080518 A310076

Adjacent sequences: A175310 A175311 A175312 * A175314 A175315 A175316

Keyword

nonn

Author

John W. Layman, Mar 31 2010

Status

approved