

A061794


Number of distinct sums d(i) + d(j) for 1<=i<=j<=n, d(k) = A000005(k) = number of divisors function.


0



1, 3, 3, 5, 5, 7, 7, 7, 7, 7, 7, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..73.


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 tauvalues gives results falling between these two extremes. E.g. n=10, A000005:{1,2,2,3,2,4,2,4,3,4...}; possible values of sum of 2:{2,3,4,5,6,7,8}, thus a(10)=7.


MATHEMATICA

f[x_] := DivisorSigma[0, x] t0=Table[Length[Union[Flatten[Table[f[u]+f[w], {w, 1, m}, {u, 1, m}]]]], {m, 1, 75}]


CROSSREFS

A000217, A000005.
Sequence in context: A085779 A078936 A293702 * A088524 A129337 A133909
Adjacent sequences: A061791 A061792 A061793 * A061795 A061796 A061797


KEYWORD

nonn


AUTHOR

Labos Elemer, Jun 22 2001


STATUS

approved



