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A122410
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a(n) = sum of j's for those k's, 1 <= k <= n, where GCD(k,n) = p^j, p = prime.
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1
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0, 1, 1, 3, 1, 3, 1, 7, 4, 5, 1, 8, 1, 7, 6, 15, 1, 10, 1, 14, 8, 11, 1, 18, 6, 13, 13, 20, 1, 14, 1, 31, 12, 17, 10, 26, 1, 19, 14, 32, 1, 20, 1, 32, 22, 23, 1, 38, 8, 26, 18, 38, 1, 31, 14, 46, 20, 29, 1, 36, 1, 31, 30, 63, 16, 32, 1, 50, 24, 34, 1, 58, 1, 37, 32, 56, 16, 38, 1, 68, 40
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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EXAMPLE
| The positive integers k, k <= 12, where GCD(k,12) = a power of a prime, are 1,2, 3,4,8,9 and 10. GCD(1,12) = p^0, GCD(2,12) = 2^1, GCD(3,12) = 3^1, GCD(4,12) = 2^2, GCD(8,12) = 2^2, GCD(9,12) = 3^1 and GCD(10,12) = 2^1. The sum of the exponents raising the primes is 0+1+1+2+2+1+1 = 8. So a(12) = 8.
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MATHEMATICA
| f[n_] := Plus @@ Last /@ Flatten[Select[FactorInteger[GCD[Range[n], n]], Length[ # ] == 1 &], 1]; Table[f[n], {n, 80}] (*Chandler*)
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CROSSREFS
| Cf. A122411.
Sequence in context: A095250 A135521 A176032 * A082495 A200476 A016572
Adjacent sequences: A122407 A122408 A122409 * A122411 A122412 A122413
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Sep 02 2006
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EXTENSIONS
| Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 06 2006
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