login
A072301
Number of positive integers not exceeding n that are relatively prime to sigma(n).
0
1, 2, 2, 4, 2, 2, 4, 5, 9, 3, 4, 5, 6, 5, 5, 16, 6, 11, 8, 6, 11, 7, 8, 7, 25, 8, 11, 12, 8, 10, 16, 19, 11, 11, 12, 29, 18, 10, 17, 10, 12, 14, 20, 13, 14, 15, 16, 23, 31, 33, 17, 22, 18, 15, 19, 15, 23, 15, 16, 17, 30, 21, 30, 64, 19, 22, 32, 20, 23, 23, 24, 35, 36, 24, 37, 26, 26
OFFSET
1,2
FORMULA
a(n) = Sum_{d|sigma(n)} moebius(d)*floor(n/d). - Ridouane Oudra, May 12 2024
EXAMPLE
Among the positive integers not exceeding 12, the five numbers 1,3,5,9,11 are relatively prime to sigma(12)=28. Hence a(12)=5.
MAPLE
with(numtheory) : seq(add(mobius(d)*floor(n/d), d in divisors(sigma(n))) , n=1..100) ; # Ridouane Oudra, May 12 2024
MATHEMATICA
r = {}; Do[ s = DivisorSigma[1, n]; j = 0; For[i = 1, i <= n, i++, If[GCD[s, i] == 1, j++ ]]; r = Append[r, j], {n, 1, 10^2}]; r
CROSSREFS
Cf. A000203.
Sequence in context: A309709 A143230 A276604 * A127171 A215655 A118232
KEYWORD
base,nonn
AUTHOR
Joseph L. Pe, Jul 14 2002
STATUS
approved