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A008475
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If n = Product (p_j^k_j) then a(n) = Sum (p_j^k_j) (a(1) = 0 by convention).
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36
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0, 2, 3, 4, 5, 5, 7, 8, 9, 7, 11, 7, 13, 9, 8, 16, 17, 11, 19, 9, 10, 13, 23, 11, 25, 15, 27, 11, 29, 10, 31, 32, 14, 19, 12, 13, 37, 21, 16, 13, 41, 12, 43, 15, 14, 25, 47, 19, 49, 27, 20, 17, 53, 29, 16, 15, 22, 31, 59, 12, 61, 33, 16, 64, 18, 16, 67, 21, 26, 14, 71, 17, 73
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) is the minimal number m such that the symmetric group S_m has an element of order n - Ahmed Fares (ahmedfares(AT)my-deja.com), Jun 26 2001
a(A000961(n)) = A000961(n); a(A005117(n)) = A001414(A005117(n)).
If gcd[u,w]=1, then a[u.w]=a[u]+a[w]; behaves like logarithm; compare A001414 or A056239. - Labos E. (labos(AT)ana.sote.hu), Mar 31 2003
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REFERENCES
| J. Bamberg, G. Cairns and D. Kilminster, The crystallographic restriction, permutations and Goldbach's conjecture, Amer. Math. Monthly, 110 (March 2003), 202-209.
F. J. Budden, The Fascination of Groups, Cambridge, 1972; pp. 322, 573.
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LINKS
| Daniel Forgues, Table of n, a(n) for n=1..100000
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FORMULA
| Additive with a(p^e) = p^e.
a(n) = sum (A027748(n,k) ^ A124010(n,k): k = 1, ... ,A001221(n)), for n>1. [Reinhard Zumkeller, Oct 10 2011]
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EXAMPLE
| a(180) = a(2^2 * 3^2 * 5) = 2^2 + 3^2 + 5 = 18.
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MAPLE
| A008475 := proc(n) local e, j; e := ifactors(n)[2]:
add (e[j][1]^e[j][2], j=1..nops(e)) end:
seq (A008475(n), n=1..60);
# - Peter Luschny, Jan 17 2010
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MATHEMATICA
| f[n_] := Plus @@ Power @@@ FactorInteger@ n; f[1] = 0; Array[f, 73]
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PROG
| (PARI) for(n=1, 100, print1(sum(i=1, omega(n), component(component(factor(n), 1), i)^component(component(factor(n), 2), i)), ", "))
(PARI) a(n)=local(t); if(n<1, 0, t=factor(n); sum(k=1, matsize(t)[1], t[k, 1]^t[k, 2])) /* Michael Somos Oct 20 2004 */
(Haskell)
a008475 1 = 0
a008475 n = sum $ zipWith (^) (a027748_row n) (a124010_row n)
-- Reinhard Zumkeller, Oct 10 2011
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CROSSREFS
| Cf. A001414, A000961, A005117, A051613.
Cf. A081402-A081404.
Cf. A027748, A124010, A001221.
Sequence in context: A130044 A156229 A082081 * A161656 A162683 A073137
Adjacent sequences: A008472 A008473 A008474 * A008476 A008477 A008478
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KEYWORD
| nonn,nice
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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