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A279436 Number of nonprimes less than or equal to n that do not divide n. 1
0, 0, 0, 0, 1, 1, 2, 1, 3, 4, 5, 3, 6, 6, 7, 6, 9, 7, 10, 8, 11, 12, 13, 9, 14, 15, 15, 15, 18, 15, 19, 16, 20, 21, 22, 18, 24, 24, 25, 22, 27, 24, 28, 26, 27, 30, 31, 25, 32, 31, 34, 33, 36, 32, 37, 34, 39, 40, 41, 34, 42, 42, 41, 40, 45, 43, 47, 45, 48, 46, 50, 42, 51, 51, 50, 51, 54, 52, 56, 50, 55, 58, 59, 52, 60, 61, 62, 59, 64, 57, 65, 64, 67, 68, 69, 62, 71, 69, 70, 68 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

FORMULA

G.f.: A(x) = B(x) + C(x) - D(x), where B(x) = Sum_{k>=1} x^(2*k+1)/((1 - x^k)*(1 - x^(k+1))), C(x) = Sum_{k>=1} x^prime(k)/(1 - x^prime(k)), D(x) = Sum_{k>=1} x^prime(k)/(1 - x).

a(n) = n - A000720(n) - A000005(n) + A001221(n).

a(n) = A062298(n) - A033273(n).

a(n) = A049820(n) - A048865(n).

a(n) = A229109(n) - A082514(n).

a(A000040(n)) = A065890(n).

a(A000040(n)) + 1 = A014689(n).

A000040(n) - a(A000040(n)) = n + 1.

EXAMPLE

a(10) = 4 because 10 has 4 divisors {1,2,5,10} therefore 6 non-divisors {3,4,6,7,8,9} out of which 4 are nonprimes {4,6,8,9}.

MATHEMATICA

Table[n - PrimePi[n] - DivisorSigma[0, n] + PrimeNu[n], {n, 1, 100}]

PROG

(PARI) for(n=1, 50, print1(n - primepi(n) - numdiv(n) + omega(n), ", ")) \\ G. C. Greubel, May 22 2017

(PARI) first(n)=my(v=vector(n), pp); forfactored(k=1, n, if(k[2][, 2]==[1]~, pp++); v[k[1]]=k[1] - pp - numdiv(k) + omega(k)); v \\ Charles R Greathouse IV, May 23 2017

(Python)

from sympy import primepi, divisor_count, primefactors

def a(n): return 0 if n==1 else n - primepi(n) - divisor_count(n) + len(primefactors(n)) # Indranil Ghosh, May 23 2017

CROSSREFS

Cf. A000005, A000040, A000720, A001221, A014689, A033273, A048865, A049820, A062298, A065890, A082514, A229109.

Sequence in context: A256100 A117407 A232095 * A082470 A101204 A169808

Adjacent sequences:  A279433 A279434 A279435 * A279437 A279438 A279439

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Dec 12 2016

STATUS

approved

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Last modified December 15 22:53 EST 2018. Contains 318157 sequences. (Running on oeis4.)