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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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5
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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.) [From Daniel Forgues (squid(AT)zensearch.com), Nov 17 2009]
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,1000
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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}](* From Jean-François Alcover, Nov 14 2011 *)
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PROG
| (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) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Sep 15 2009]
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CROSSREFS
| Cf. A064476, A064479, A003958. Apart from initial terms, same as A003959.
Sequence in context: A091205 A106447 A060866 * A111798 A115305 A098550
Adjacent sequences: A064475 A064476 A064477 * A064479 A064480 A064481
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Oct 06 2001
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Oct 06 2001
Edited by Daniel Forgues, Nov 18 2009
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