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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
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
Sequence in context: A230070 A224762 A039776 * A003139 A349918 A244797
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 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)