A064478 If n = Product p(k)^e(k) then a(n) = Product (p(k)+1)^e(k), a(0) = 1, a(1)=2.

1, 2, 3, 4, 9, 6, 12, 8, 27, 16, 18, 12, 36, 14, 24, 24, 81, 18, 48, 20, 54, 32, 36, 24, 108, 36, 42, 64, 72, 30, 72, 32, 243, 48, 54, 48, 144, 38, 60, 56, 162, 42, 96, 44, 108, 96, 72, 48, 324, 64, 108, 72, 126, 54, 192, 72, 216, 80, 90, 60, 216, 62, 96, 128, 729, 84, 144

Offset

0,2

Comments

a(0)=1 and a(1)=2 by convention (which makes a(n) not multiplicative).

The alternate convention a(0)=0 and a(1)=1 would have made a(n) completely multiplicative (cf. A003959 for completely multiplicative version.) - Daniel Forgues, Nov 17 2009

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

Maple

a:= n-> `if`(n<2, n+1, mul((i[1]+1)^i[2], i=ifactors(n)[2])):
seq(a(n), n=0..80);  # Alois P. Heinz, Sep 13 2017

Mathematica

a[0] = 1; a[1] = 2; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]]+1)^fi[[All, 2]])); Table[a[n], {n, 0, 66}](* Jean-François Alcover, Nov 14 2011 *)
f[n_] := Times @@ ((1 + #[[1]])^#[[2]] & /@ FactorInteger@ n); Array[f, 67, 0] (* Robert G. Wilson v, Sep 13 2017 *)

Prog

(PARI) a(n) = if(n<=1, n + 1, my(f=factor(n)); prod(i=1, #f~, (1 + f[i, 1])^f[i, 2])) \\ Harry J. Smith, Sep 15 2009
(Haskell)
a064478 n = if n <= 1 then n + 1 else a003959 n
-- Reinhard Zumkeller, Feb 28 2013

Crossrefs

Cf. A064476, A064479, A003958. Apart from initial terms, same as A003959.

Sequence in context: A234742 A277711 A060866 * A111798 A375015 A249543

Adjacent sequences: A064475 A064476 A064477 * A064479 A064480 A064481

Keyword

nonn,nice,easy

Author

N. J. A. Sloane, Oct 06 2001

Extensions

More terms from Vladeta Jovovic, Oct 06 2001

Edited by Daniel Forgues, Nov 18 2009

Status

approved