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A064478
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If n = Product p(k)^e(k) then a(n) = Product (p(k)+1)^e(k), a(0) = 1, a(1)=2.
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8
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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
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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MAPLE
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a:= n-> `if`(n<2, n+1, mul((i[1]+1)^i[2], i=ifactors(n)[2])):
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MATHEMATICA
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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 *)
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PROG
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(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
(Haskell)
a064478 n = if n <= 1 then n + 1 else a003959 n
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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