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A139130 a(n) = sum{k=1 to n} d(d(k)), where d(k) = number of divisors of k. 2

%I

%S 1,3,5,7,9,12,14,17,19,22,24,28,30,33,36,38,40,44,46,50,53,56,58,62,

%T 64,67,70,74,76,80,82,86,89,92,95,98,100,103,106,110,112,116,118,122,

%U 126,129,131,135,137,141,144,148,150,154,157,161,164,167,169,175,177,180

%N a(n) = sum{k=1 to n} d(d(k)), where d(k) = number of divisors of k.

%D R. Bellman and H. N. Shapiro, On a problem in additive number theory, Annals Math., 49 (1948), 333-340. See Eq. 1.6. [From _N. J. A. Sloane_, Mar 12 2009]

%H Alois P. Heinz, <a href="/A139130/b139130.txt">Table of n, a(n) for n = 1..1000</a>

%p with(numtheory): a:= n-> add(tau(tau (k)), k=1..n): seq(a(n), n=1..70); # _Alois P. Heinz_, Aug 28 2008

%t Table[Sum[DivisorSigma[0,DivisorSigma[0,k]],{k,1,n}],{n,1,62}] (* _Geoffrey Critzer_, Sep 28 2013 *)

%o (PARI) a(n) = sum(k = 1, n, numdiv(numdiv(k))); \\ _Michel Marcus_, Sep 28 2013

%Y Cf. A010553, A006218.

%K nonn

%O 1,2

%A _Leroy Quet_, Jun 05 2008

%E More terms from _Alois P. Heinz_, Aug 28 2008

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Last modified July 28 00:54 EDT 2021. Contains 346316 sequences. (Running on oeis4.)