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A048864
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Number of nonprime numbers (composites and 1) in the reduced residue system of n.
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14
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1, 1, 1, 1, 2, 1, 3, 1, 3, 2, 6, 1, 7, 2, 4, 3, 10, 1, 11, 2, 6, 4, 14, 1, 12, 5, 10, 5, 19, 1, 20, 6, 11, 7, 15, 3, 25, 8, 14, 6, 28, 2, 29, 8, 12, 10, 32, 3, 28, 7, 19, 11, 37, 4, 26, 10, 22, 14, 42, 2, 43, 14, 20, 15, 32, 5, 48, 15, 27, 8, 51, 6, 52, 17, 21, 17, 41, 6, 57, 12, 33, 20
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OFFSET
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1,5
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COMMENTS
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Differs from A039776 at n = 20, 21, ...
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LINKS
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Michael De Vlieger, Table of n, a(n) for n = 1..10000
Abhijit A J, A. Satyanarayana Reddy, Number of non-primes in the set of units modulo n, arXiv:1907.09908 [math.GM], 2019.
Abhijit A. J. and A. Satyanarayana Reddy, Number of non-primes in the set of units modulo n, The Mathematics Student, Vol. 88, No. 1-2 (2019), 147-152.
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FORMULA
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a(n) = A036997(n) + 1. - Peter Luschny, Oct 22 2010
a(n) = A000010(n) - (A000720(n) - A001221(n)).
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EXAMPLE
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At n = 10, we see that the numbers below 10 coprime to 10 are 1, 3, 7, 9. Removing 3 and 7, which are prime, we are left with two numbers, 1 and 9. Hence a(10) = 2.
At n = 100, phi(100) = 40, phi(100) - (pi(100) - A001221(100)) = 17, thus a(100) = 17.
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MAPLE
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A048864 := n -> nops(select(k->gcd(k, n)=1, remove(isprime, [$1..n]))); # Peter Luschny, Oct 22 2010
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MATHEMATICA
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Array[EulerPhi@ # - (PrimePi@ # - PrimeNu@ #) &, 82] (* Michael De Vlieger, Jul 03 2016 *)
Table[Length[Select[Range[n], GCD[n, #] == 1 && Not[PrimeQ[#]] &]], {n, 80}] (* Alonso del Arte, Oct 02 2017 *)
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PROG
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(PARI) a(n) = eulerphi(n) - (primepi(n) - omega(n)); \\ Indranil Ghosh, Apr 27 2017
(Python)
from sympy import totient, primepi, primefactors
def a(n): return totient(n) - (primepi(n) - len(primefactors(n))) # Indranil Ghosh, Apr 27 2017
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CROSSREFS
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Cf. A039776, A000010, A000720, A001221, A037228, A072022, A072023, A074915.
Sequence in context: A230070 A224762 A039776 * A003139 A349918 A244797
Adjacent sequences: A048861 A048862 A048863 * A048865 A048866 A048867
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KEYWORD
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nonn
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AUTHOR
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Labos Elemer
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EXTENSIONS
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Converted second formula to an equation, added commas to the example - R. J. Mathar, Oct 23 2010
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STATUS
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approved
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