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

1,2

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

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).

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 *)

Prog

(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

Crossrefs

Cf. A003961, A000005.

Sequence in context: A092996 A141264 A062949 * A081500 A338655 A030365

Adjacent sequences: A166648 A166649 A166650 * A166652 A166653 A166654

Keyword

nonn,mult

Author

Jaroslav Krizek, Oct 18 2009

Status

approved