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%I #23 Aug 28 2023 08:23:11
%S 1,7,10,27,16,70,22,83,55,112,34,270,40,154,160,227,52,385,58,432,220,
%T 238,70,830,141,280,244,594,88,1120,94,579,340,364,352,1485,112,406,
%U 400,1328,124,1540,130,918,880,490,142,2270,267,987,520,1080,160,1708
%N a(n) = Sum_{i|n, j|n} lcm(i,j).
%H Harry J. Smith, <a href="/A064950/b064950.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = Sum_{d|n} d*tau(d^2).
%F Multiplicative with a(p^e) = (p^(e+2) - 3*p^(e+1) + p + 1 + 2*p^(e+2)*e - 2*p^(e+1)*e)/(p-1)^2.
%t a[n_]:= Sum[LCM[i,j], {i, Divisors[n]}, {j, Divisors[n]}];
%t Array[a,60] (* _Jean-François Alcover_, Jun 03 2019 *)
%t f[p_, e_] := (p^(e+2) - 3*p^(e+1) + p + 1 + 2*p^(e+2)*e - 2*p^(e+1)*e)/(p-1)^2; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 60] (* _Amiram Eldar_, Aug 28 2023 *)
%o (PARI) for (n=1, 1000, d=divisors(n); a=sum(i=1, length(d), numdiv(d[i]^2)*d[i]); write("b064950.txt", n, " ", a)) \\ _Harry J. Smith_, Oct 01 2009
%o (Sage)
%o def A064950(n) :
%o tau = sloane.A000005; D = divisors(n)
%o return reduce(lambda x,y: x+y, [d*tau(d^2) for d in D])
%o [A064950(n) for n in (1..54)] # _Peter Luschny_, Sep 10 2012
%Y Cf. A060724, A000005, A062369, A062368, A062380.
%K mult,nonn,easy
%O 1,2
%A _Vladeta Jovovic_, Oct 28 2001
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