|
%I #16 May 21 2016 17:23:17
%S 1,3,5,9,9,15,13,27,25,27,21,45,25,39,45,81,33,75,37,81,65,63,45,135,
%T 81,75,125,117,57,135,61,243,105,99,117,225,73,111,125,243,81,195,85,
%U 189,225,135,93,405,169,243
%N Totally multiplicative sequence with a(p) = 2p-1 for prime p.
%C Maximum number of divisors for m^2 when m has exactly n divisors. - _Franklin T. Adams-Watters_, Jan 08 2016
%H G. C. Greubel, <a href="/A166651/b166651.txt">Table of n, a(n) for n = 1..10000</a>
%F Multiplicative with a(p^e) = (2p-1)^e. If n = Product p(k)^e(k) then a(n) = Product (2*p(k)-1)^e(k).
%t a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((2*fi[[All, 1]] - 1)^fi[[All, 2]])); Table[a[n], {n, 1, 100}] (* _G. C. Greubel_, May 21 2016 *)
%o (PARI) a(n) = {my(f = factor(n)); for (i=1, #f~, f[i,1] = (2*f[i,1]-1)^f[i,2]; f[i,2] = 1;); factorback(f);} \\ _Michel Marcus_, Jan 09 2016
%Y Cf. A003961, A000005.
%K nonn,mult
%O 1,2
%A _Jaroslav Krizek_, Oct 18 2009
|
