login
A175313
Number of distinct sums of pairs of reciprocals of 1,2,3,...,n.
1
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
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 A375999 A080518
KEYWORD
nonn
AUTHOR
John W. Layman, Mar 31 2010
STATUS
approved