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%I #22 Mar 23 2023 07:50:37
%S 1,4,6,16,10,24,14,64,36,40,22,96,26,56,60,256,34,144,38,160,84,88,46,
%T 384,100,104,216,224,58,240,62,1024,132,136,140,576,74,152,156,640,82,
%U 336,86,352,360,184,94,1536,196,400,204,416,106,864,220,896,228,232,118
%N a(n) = n * 2^bigomega(n).
%C Rearrangement of A123666.
%H G. C. Greubel, <a href="/A123667/b123667.txt">Table of n, a(n) for n = 1..5000</a>
%F Totally multiplicative with a(p) = 2p, p prime.
%F a(n) = n * A061142(n).
%F Dirichlet g.f.: Product_{p prime} 1 / (1 - 2 * p^(1 - s)). - _Ilya Gutkovskiy_, Oct 29 2019
%p A123667:=n->n*2^numtheory[bigomega](n): seq(A123667(n), n=1..100); # _Wesley Ivan Hurt_, Apr 09 2017
%t Table[n*2^PrimeOmega[n],{n,60}] (* _Harvey P. Dale_, Jun 11 2014 *)
%o (PARI) a(n) = n*2^bigomega(n); \\ _Michel Marcus_, Apr 10 2017
%Y Cf. A061142, A001222 (bigomega), A123666.
%K nonn,mult
%O 1,2
%A _Franklin T. Adams-Watters_, Oct 04 2006
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