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A008474
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If n = Product (p_j^k_j) then a(n) = Sum (p_j + k_j).
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12
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0, 3, 4, 4, 6, 7, 8, 5, 5, 9, 12, 8, 14, 11, 10, 6, 18, 8, 20, 10, 12, 15, 24, 9, 7, 17, 6, 12, 30, 13, 32, 7, 16, 21, 14, 9, 38, 23, 18, 11, 42, 15, 44, 16, 11, 27, 48, 10, 9, 10, 22, 18, 54, 9, 18, 13, 24, 33, 60, 14, 62, 35, 13, 8, 20, 19, 68, 22, 28, 17, 72, 10, 74, 41, 11, 24, 20, 21
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(1) = 0 by convention, but could equally be taken to be 1 or 2.
Since only the primes p_j with nonzero exponents k_j in the factorization of n are considered in Sum (p_j + k_j), to the empty product (1) should correspond the empty sum (0). a(1) = 0 is thus the most natural choice. [From Daniel Forgues, Apr 06 2010]
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Prime Factorization
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FORMULA
| Additive with a(p^e) = p + e.
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MAPLE
| A008474 := proc(n) local e, j; e := ifactors(n)[2]:
add(e[j][1]+e[j][2], j=1..nops(e)) end:
seq (A008474(n), n=1..60);
# - Peter Luschny, Jan 17 2011
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MATHEMATICA
| A008474[n_]:=Plus@@Flatten[FactorInteger[n]]; Table[A008474[n], {n, 200}] (* Zak Seidov *)
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PROG
| (Haskell)
a008474 n = sum $
zipWith (+) (a027748_row n) (map fromIntegral $ a124010_row n)
-- Reinhard Zumkeller, Feb 11 2012, Aug 27 2011
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CROSSREFS
| Cf. A107737, A107738.
Cf. A000026.
Cf. A027748, A124010.
Sequence in context: A120613 A164326 A117571 * A111611 A100478 A112376
Adjacent sequences: A008471 A008472 A008473 * A008475 A008476 A008477
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KEYWORD
| nonn,changed
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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EXTENSIONS
| More terms from Zak Seidov (zakseidov(AT)yahoo.com), May 23 2005
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