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A139555
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a(n) = number of prime-powers (including 1) that each are <= n and are coprime to n.
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4
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1, 1, 2, 2, 4, 2, 5, 4, 6, 4, 8, 4, 9, 6, 7, 7, 11, 6, 12, 8, 10, 8, 13, 8, 13, 10, 13, 11, 16, 8, 17, 14, 15, 13, 16, 11, 19, 14, 16, 13, 20, 12, 21, 16, 17, 16, 22, 15, 22, 17, 20, 18, 24, 17, 22, 18, 21, 19, 25, 16, 26, 21, 22, 22, 25, 18, 28, 22, 25, 19, 29, 21, 30, 24, 26, 24
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Indices of first occurrence of each natural number: 1, 3, 5, 7, 9, 15, 11, 13, 21, 17, 19, 23, 32, 33, ..., . - Robert G. Wilson v.
Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 27 2010: (Start)
a(n) <= A000010(n); a(A051250(n)) = A000010(A051250(n)), 1<=n<=17;
conjecture: a(n) < A000010(n) for n > 60, cf. A051250. (End)
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..1000 [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 27 2010]
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EXAMPLE
| All the positive integers <= 21 that are coprime to 21 are 1,2,4,5,8,10,11,13,16,17,19,20. Of these integers, only 1,2,4,5,8,11,13,16,17,19 are prime-powers. There are 10 of these prime-powers; so a(21) = 10.
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MAPLE
| isA000961 := proc(n) if n = 1 or isprime(n) then true; else RETURN(nops(ifactors(n)[2]) =1) ; fi ; end: A139555 := proc(n) local a, i; a := 0 ; for i from 1 to n do if isA000961(i) and gcd(i, n) = 1 then a := a+1 ; fi ; od: a ; end: seq(A139555(n), n=1..100) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 12 2008
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MATHEMATICA
| f[n_] := Length@ Select[Range@ n, Length@ FactorInteger@ # == 1 == GCD[n, # ] &]; Array[f, 76] (* Robert G. Wilson v *)
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PROG
| Contribution from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 27 2010: (Start)
(Other) Haskell:
a139555 n = length . filter isPrimePower $ totatives n
........... where isPrimePower m = a001221 m <= 1
................. totatives m = filter ((== 1) . (gcd m)) [1..m]
-- eop. (End)
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CROSSREFS
| Cf. A139556.
Cf. A065515. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 27 2010]
Sequence in context: A129296 A125296 A121895 * A088371 A133181 A179013
Adjacent sequences: A139552 A139553 A139554 * A139556 A139557 A139558
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet Apr 27 2008
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl) and Robert G. Wilson v, (rgwv(AT)rgwv.com), May 12 2008
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