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%I #30 Oct 23 2022 02:54:32
%S 1,2,3,6,5,6,7,18,12,10,11,18,13,14,15,54,17,24,19,30,21,22,23,54,30,
%T 26,48,42,29,30,31,162,33,34,35,72,37,38,39,90,41,42,43,66,60,46,47,
%U 162,56,60,51,78,53,96,55,126,57,58,59,90,61,62,84,486,65,66,67,102,69
%N Möbius transform of A003959.
%C a(n) = n for squarefree n; otherwise, a(n) > n. - _Ivan Neretin_, May 13 2015
%C Dirichlet inverse of A062953. - _Werner Schulte_, Oct 25 2018
%H Ivan Neretin, <a href="/A003968/b003968.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = p(p+1)^(e-1). - _David W. Wilson_, Sep 01 2001
%F Sum_{k=1..n} a(k) ~ c * n^2, where c = (1/2) * Product_{p prime} (1 + 1/(p^3 - p^2 - p)) = A104141/A005596 = 0.8128327996... . - _Amiram Eldar_, Oct 23 2022
%t Table[{pp, aa} = Transpose[FactorInteger[n]]; Times @@ (pp*(pp + 1)^(aa - 1)), {n, 70}] (* _Ivan Neretin_, May 13 2015 *)
%o (PARI) a(n) = {my(f=factor(n)); for (i=1, #f~, p= f[i, 1]; f[i, 1] = p*(p+1)^(f[i,2]-1); f[i, 2] = 1); factorback(f);} \\ _Michel Marcus_, Feb 26 2015
%Y Cf. A003959, A005596, A062953, A104141.
%K nonn,mult
%O 1,2
%A _Marc LeBrun_
%E More terms from _David W. Wilson_, Aug 29 2001
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