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 A048864 Number of nonprime numbers (composites and 1) in the reduced residue system of n. 14
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS Differs from A039776 at n = 20, 21, ... LINKS 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. FORMULA a(n) = A036997(n) + 1. - Peter Luschny, Oct 22 2010 a(n) = A000010(n) - (A000720(n) - A001221(n)). EXAMPLE 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. MAPLE A048864 := n -> nops(select(k->gcd(k, n)=1, remove(isprime, [\$1..n]))); # Peter Luschny, Oct 22 2010 MATHEMATICA 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 *) PROG (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 CROSSREFS 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 KEYWORD nonn AUTHOR EXTENSIONS Converted second formula to an equation, added commas to the example - R. J. Mathar, Oct 23 2010 STATUS approved

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Last modified March 28 03:48 EDT 2023. Contains 361577 sequences. (Running on oeis4.)