A061796 Number of distinct sums sigma(i) + sigma(j) for 1<=i<=j<=n, where sigma(k) = A000203(k).

1, 3, 6, 9, 12, 17, 18, 23, 27, 30, 30, 39, 40, 45, 45, 51, 51, 60, 60, 66, 69, 72, 72, 81, 81, 81, 86, 92, 94, 103, 103, 112, 112, 114, 114, 131, 133, 133, 133, 141, 141, 151, 153, 155, 157, 157, 157, 175, 178, 185, 185, 193, 193, 202, 202, 202, 205, 205, 205

Offset

1,2

Links

Table of n, a(n) for n=1..59.

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 sigma-values gives results falling between these two extremes.
E.g. n=10, A000203: {1,3,4,7,6,12,8,15,13,18...}. The 55 possible sigma(i)+sigma(j) additions give 30 different results: {2,4,5,6,...,33,36}. Therefore a(10)=30.

Mathematica

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

Crossrefs

Cf. A000217, A000203.

Sequence in context: A072567 A186353 A362032 * A113241 A310153 A356104

Adjacent sequences: A061793 A061794 A061795 * A061797 A061798 A061799

Keyword

nonn

Author

Labos Elemer, Jun 22 2001

Status

approved