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Totally multiplicative sequence with a(p) = 8p for prime p.
1

%I #13 Oct 30 2019 12:34:35

%S 1,16,24,256,40,384,56,4096,576,640,88,6144,104,896,960,65536,136,

%T 9216,152,10240,1344,1408,184,98304,1600,1664,13824,14336,232,15360,

%U 248,1048576,2112,2176,2240,147456,296,2432,2496,163840,328,21504,344,22528

%N Totally multiplicative sequence with a(p) = 8p for prime p.

%H G. C. Greubel, <a href="/A166629/b166629.txt">Table of n, a(n) for n = 1..10000</a>

%F Multiplicative with a(p^e) = (8p)^e.

%F If n = Product p(k)^e(k) then a(n) = Product (8*p(k))^e(k).

%F a(n) = n * A165829(n) = n * 8^bigomega(n) = n * 8^A001222(n).

%F Dirichlet g.f.: Product_{p prime} 1 / (1 - 8 * p^(1 - s)). - _Ilya Gutkovskiy_, Oct 30 2019

%t Table[n*8^PrimeOmega[n], {n, 1, 100}] (* _G. C. Greubel_, May 19 2016 *)

%o (PARI) a(n) = n*8^bigomega(n); \\ _Michel Marcus_, Oct 30 2019

%Y Cf. A001222, A165829.

%K nonn,mult

%O 1,2

%A _Jaroslav Krizek_, Oct 18 2009