A166651 Totally multiplicative sequence with a(p) = 2p-1 for prime p.

1, 3, 5, 9, 9, 15, 13, 27, 25, 27, 21, 45, 25, 39, 45, 81, 33, 75, 37, 81, 65, 63, 45, 135, 81, 75, 125, 117, 57, 135, 61, 243, 105, 99, 117, 225, 73, 111, 125, 243, 81, 195, 85, 189, 225, 135, 93, 405, 169, 243

Offset: 1

Author

Jaroslav Krizek, Oct 18 2009

Keywords

• nonn
• mult

Comments

Maximum number of divisors for m^2 when m has exactly n divisors. - Franklin T. Adams-Watters, Jan 08 2016

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003961, A000005.

Programs

Mathematica

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 *)

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

Formula

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).