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Search: id:A034448
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| A034448 |
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usigma(n) = sum of unitary divisors of n (divisors d such that gcd(d, n/d)=1). |
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+0
92
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| 1, 3, 4, 5, 6, 12, 8, 9, 10, 18, 12, 20, 14, 24, 24, 17, 18, 30, 20, 30, 32, 36, 24, 36, 26, 42, 28, 40, 30, 72, 32, 33, 48, 54, 48, 50, 38, 60, 56, 54, 42, 96, 44, 60, 60, 72, 48, 68, 50, 78, 72, 70, 54, 84, 72, 72, 80, 90, 60, 120, 62, 96, 80, 65, 84, 144, 68, 90, 96, 144
(list; graph; listen)
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OFFSET
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1,2
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
S. R. Finch, Unitarism and infinitarism.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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If n = Product p_i^e_i, usigma(n) = Product (p_i^e_i + 1) - Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 19 2001
Dirichlet generating function: zeta(s)*zeta(s-1)/zeta(2s-1) (should be checked!). - Franklin T. Adams-Watters, Sep 11 2005.
Multiplicative with a(p^e) = p^e+1 for e>0. - Franklin T. Adams-Watters, Sep 11 2005.
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EXAMPLE
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Unitary divisors of 12 are 1, 3, 4, 12. Or, 12=3*2^2 hence usigma(12)=(3+1)*(2^2+1)=20.
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MAPLE
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A034448 := proc(n) local ans, i:ans := 1: for i from 1 to nops(ifactors(n)[ 2 ]) do ans := ans*(1+ifactors(n)[ 2 ][ i ][ 1 ]^ifactors(n)[ 2 ] [ i ] [ 2 ]): od: RETURN(ans) end:
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MATHEMATICA
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usigma[n_] := Block[{d = Divisors[n]}, Plus @@ Select[d, GCD[ #, n/# ] == 1 &]]; Table[ usigma[n], {n, 71}] (from Robert G. Wilson v Aug 28 2004)
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PROGRAM
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(PARI) a(n) = sumdiv(n, d, if(gcd(d, n/d)==1, d)) (Rick L. Shepherd)
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CROSSREFS
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Cf. A034444, A034460, A047994, A048250, A064000.
Sequence in context: A047425 A048989 A103402 this_sequence A107752 A069184 A049417
Adjacent sequences: A034445 A034446 A034447 this_sequence A034449 A034450 A034451
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KEYWORD
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nonn,easy,nice,mult
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AUTHOR
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njas
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EXTENSIONS
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More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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