A283190 - OEIS

A283190

a(n) is the number of different values n mod k for 1 <= k <= floor(n/2).

0, 1, 1, 1, 2, 1, 2, 2, 2, 3, 4, 2, 3, 3, 3, 4, 5, 4, 5, 4, 4, 5, 6, 5, 6, 7, 7, 7, 8, 6, 7, 7, 7, 8, 9, 8, 9, 9, 9, 10, 11, 9, 10, 9, 9, 10, 11, 10, 11, 12, 12, 12, 13, 12, 13, 13, 13, 14, 15, 13, 14, 14, 14, 15, 16, 15, 16, 15, 15, 16, 17, 16, 17, 17, 17, 17, 18, 17

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OFFSET

1,5

COMMENTS

a(n) is the number of distinct terms in the first half of the n-th row of the A048158 triangle. - Michel Marcus, Mar 04 2017

a(n)/n appears to converge to a constant, approximately 0.2296. Can this be proved, and does the constant have a closed form? - Robert Israel, Mar 13 2017

The constant that a(n)/n approaches is Sum {p prime} 1/(p^2+p)* Product {q prime < p} (q-1)/q. - Michael R Peake, Mar 16 2017

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Michael R Peake, Explanation of limiting value of a(n)/n

EXAMPLE

a(7) = 2 because 7=0 (mod 1), 7=1 (mod 2), 7=1 (mod 3), two different results.

MAPLE

N:= 100: # to get a(1)..a(N)

V:= Vector(N, 1):

V[1]:= 0:

for m from 2 to N-1 do

k:= m/min(numtheory:-factorset(m));