

A283190


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


1



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 nth 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} (q1)/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 N1 do
k:= m/min(numtheory:factorset(m));
ns:= [seq(n, n=m+1..min(N, m+k1))];
V[ns]:= map(`+`, V[ns], 1);
od:
convert(V, list); # Robert Israel, Mar 13 2017


MATHEMATICA

Table[Length@ Union@ Map[Mod[n, #] &, Range@ Floor[n/2]], {n, 78}] (* Michael De Vlieger, Mar 03 2017 *)


PROG

(PARI) a(n) = #vecsort(vector(n\2, k, n % k), , 8); \\ Michel Marcus, Mar 02 2017


CROSSREFS

Cf. A048158.
Sequence in context: A123505 A320779 A114920 * A030361 A060715 A108954
Adjacent sequences: A283187 A283188 A283189 * A283191 A283192 A283193


KEYWORD

nonn


AUTHOR

Thomas Kerscher, Mar 02 2017


STATUS

approved



