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A064478 If n = Product p(k)^e(k) then a(n) = Product (p(k)+1)^e(k), a(0) = 1, a(1)=2. 6

%I

%S 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,

%T 36,42,64,72,30,72,32,243,48,54,48,144,38,60,56,162,42,96,44,108,96,

%U 72,48,324,64,108,72,126,54,192,72,216,80,90,60,216,62,96,128,729,84,144

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

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

%C 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

%H Harry J. Smith, <a href="/A064478/b064478.txt">Table of n, a(n) for n = 0..1000</a>

%p a:= n-> `if`(n<2, n+1, mul((i[1]+1)^i[2], i=ifactors(n)[2])):

%p seq(a(n), n=0..80); # _Alois P. Heinz_, Sep 13 2017

%t 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-Fran├žois Alcover_, Nov 14 2011 *)

%t f[n_] := Times @@ ((1 + #[[1]])^#[[2]] & /@ FactorInteger@ n); Array[f, 67, 0] (* _Robert G. Wilson v_, Sep 13 2017 *)

%o (PARI) ns(n)=local(f,p=1); f=factor(n); for(i=1, matsize(f)[1], p*=(1 + f[i, 1])^f[i, 2]); return(p) } { for (n=0, 1000, if (n>1, a=ns(n), a=n + 1); write("b064478.txt", n, " ", a) ) \\ _Harry J. Smith_, Sep 15 2009

%o (Haskell)

%o a064478 n = if n <= 1 then n + 1 else a003959 n

%o -- _Reinhard Zumkeller_, Feb 28 2013

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

%K nonn,nice,easy

%O 0,2

%A _N. J. A. Sloane_, Oct 06 2001

%E More terms from _Vladeta Jovovic_, Oct 06 2001

%E Edited by _Daniel Forgues_, Nov 18 2009

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Last modified July 18 19:00 EDT 2019. Contains 325144 sequences. (Running on oeis4.)