This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A078392 #21 May 07 2021 00:55:02
%S A078392 1,3,5,9,11,20,21,35,42,61,66,112,113,168,210,279,313,461,508,719,852,
%T A078392 1088,1277,1756,2006,2573,3106,3937,4593,5958,6872,8676,10305,12655,
%U A078392 15009,18664,21673,26559,31447,38217,44623,54386,63303,76379,89696,106879
%N A078392 Sum of GCD's of parts in all partitions of n.
%C A078392 Equals row sums of triangle A168534. - _Gary W. Adamson_, Nov 28 2009
%H A078392 Alois P. Heinz, <a href="/A078392/b078392.txt">Table of n, a(n) for n = 1..1000</a>
%F A078392 a(n) = Sum_{d|n} d * A000837(n/d).
%F A078392 a(n) = Sum_{d|n} phi(n/d)*numbpart(d) = Sum_{d|n} A000010(n/d)*A000041(d). - _Vladeta Jovovic_, May 08 2003
%F A078392 From _Richard L. Ollerton_, May 06 2021: (Start)
%F A078392 a(n) = Sum_{k=1..n} A000041(gcd(n,k)).
%F A078392 a(n) = Sum_{k=1..n} A000041(n/gcd(n,k))*A000010(gcd(n,k))/A000010(n/gcd(n,k)). (End)
%e A078392 Partitions of 4 are 1+1+1+1, 1+1+2, 2+2, 1+3, 4, the corresponding GCD's of parts are 1,1,2,1,4 and their sum is a(4) = 9.
%p A078392 with(numtheory): with(combinat):
%p A078392 a:= n-> add(phi(n/d)*numbpart(d), d=divisors(n)):
%p A078392 seq(a(n), n=1..50); # _Alois P. Heinz_, Apr 02 2015
%t A078392 a[n_] := Sum[EulerPhi[n/d]*PartitionsP[d], {d, Divisors[n]}]; Table[a[n], {n, 1, 50}] (* _Jean-François Alcover_, Jul 01 2015, after _Alois P. Heinz_ *)
%Y A078392 Cf. A000010, A000041, A168534, A181844 (the same for LCM), A319301.
%K A078392 nonn
%O A078392 1,2
%A A078392 _Vladeta Jovovic_, Dec 24 2002