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a(n) = Sum_{i=1..n} d_3(i)*d_3(i+1), where d_3(n) = A007425(n).
3

%I #16 Apr 19 2024 03:15:14

%S 3,12,30,48,75,102,132,192,246,273,327,381,408,489,624,669,723,777,

%T 831,993,1074,1101,1191,1371,1425,1515,1695,1749,1830,1911,1974,2163,

%U 2244,2325,2649,2757,2784,2865,3135,3225,3306,3387,3441,3765,3927,3954,4089,4359,4467,4629,4791,4845,4935,5205,5475

%N a(n) = Sum_{i=1..n} d_3(i)*d_3(i+1), where d_3(n) = A007425(n).

%C For background references see A330570.

%H Seiichi Manyama, <a href="/A331080/b331080.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = 3 * A331081(n). - _Amiram Eldar_, Apr 19 2024

%t f[p_, e_] := (e+1)*(e+2)/2; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; With[{t = Array[s, 100]}, Accumulate[Most[t] * Rest[t]]] (* _Amiram Eldar_, Apr 19 2024 *)

%Y Cf. A007425, A331081, A331130.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Jan 10 2020