

A139555


a(n) = number of primepowers (including 1) that each are <= n and are coprime to n.


8



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
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OFFSET

1,3


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
From Reinhard Zumkeller, 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)


LINKS

R. Zumkeller, Table of n, a(n) for n = 1..1000


FORMULA

a(n) = Sum_{k=1..A000010(n)} A010055(A038566(n,k)).  Reinhard Zumkeller, Feb 23 2012


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 primepowers. There are 10 of these primepowers; so a(21) = 10.


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, May 12 2008


MATHEMATICA

f[n_] := Length@ Select[Range@ n, Length@ FactorInteger@ # == 1 == GCD[n, # ] &]; Array[f, 76] (* Robert G. Wilson v *)


PROG

(Haskell)
a139555 = sum . map a010055 . a038566_row
 Reinhard Zumkeller, Feb 23 2012, Oct 27 2010


CROSSREFS

Cf. A139556.
Cf. A065515.  Reinhard Zumkeller, Oct 27 2010
Sequence in context: A243271 A232245 A121895 * A241814 A088371 A133181
Adjacent sequences: A139552 A139553 A139554 * A139556 A139557 A139558


KEYWORD

nonn


AUTHOR

Leroy Quet, Apr 27 2008


EXTENSIONS

More terms from R. J. Mathar and Robert G. Wilson v, May 12 2008


STATUS

approved



