A061795 Number of distinct sums phi(i) + phi(j) for 1 <= i <= j <= n, phi(k) = A000010(k).

1, 1, 3, 3, 6, 6, 9, 9, 9, 9, 13, 13, 17, 17, 18, 18, 22, 22, 26, 26, 26, 26, 30, 30, 32, 32, 32, 32, 37, 37, 41, 41, 41, 41, 43, 43, 47, 47, 47, 47, 53, 53, 57, 57, 57, 57, 62, 62, 62, 62, 63, 63, 67, 67, 67, 67, 67, 67, 72, 72, 79, 79, 79, 79, 81, 81, 86, 86, 87, 87, 93, 93

Offset

1,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Example

If the {s+t} sums are generated by adding 2 terms of an S set consisting of n different entries, then at least 1, at most n(n+1)/2 = A000217(n) distinct values can be obtained. The set of first n phi-values gives results falling between these two extremes. E.g., n=10, A000010: {1,1,2,2,4,2,6,4,6,4,...}. Additions provide {2,3,4,5,6,7,8,10,12}, i.e., 9 different results. Thus a(10)=9.

Mathematica

f[x_] := EulerPhi[x]; t0=Table[Length[Union[Flatten[Table[f[u]+f[w], {w, 1, m}, {u, 1, m}]]]], {m, 1, 75}]

Crossrefs

Cf. A000010, A000217.

Sequence in context: A023842 A165885 A227128 * A110261 A168237 A290966

Adjacent sequences: A061792 A061793 A061794 * A061796 A061797 A061798

Keyword

nonn

Author

Labos Elemer, Jun 22 2001

Status

approved