

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
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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] (* JeanFrançois 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: A310074 A310075 A233774 * A289387 A080518 A310076
Adjacent sequences: A175310 A175311 A175312 * A175314 A175315 A175316


KEYWORD

nonn


AUTHOR

John W. Layman, Mar 31 2010


STATUS

approved



