OFFSET
0,11
COMMENTS
a(p) = 0 if p is a prime. Can anyone suggest a formula?
See example for a method to find a(n). - David A. Corneth, Aug 24 2020
LINKS
David A. Corneth, Table of n, a(n) for n = 0..9999 (first 5001 terms from Alois P. Heinz)
EXAMPLE
a(14) = 4 and the partitions are (10,2,2), (8,4,2),(6,6,2) and (6,4,4).
a(13) = 0 as for all r + s + t = 13,r > 0, s > 0,t> 0 gcd(r,s,t) = 1.
From David A. Corneth, Aug 24 2020: (Start)
a(100) = 233. The squarefree part of 100 is 10. The divisors of 10 are 1, 2, 5 and 10.
These are the possible squarefree divisors of parts. As parts must not be coprime, we exclude 1, leaving 2, 5 and 10. We then compute 100/k for each of these numbers.
This gives 50, 20 and 10 respectively. Now a(100) is found by adding -(round(50^2/12)*(-1)^omega(2) + round(20^2/12)*(-1)^omega(5) + round(10^2/12)*(-1)^omega(10)) = -(-208 - 33 + 8) = 233 where omega(m) is the number of distinct divisors of m (Cf. A001221) and round(m^2/12) is the number of partitions of m into 3 parts (Cf. A069905) (End)
MATHEMATICA
a[n_] := Length[Select[Flatten[Table[{a, b, n-a-b}, {a, 1, Floor[n/3]}, {b, a, Floor[(n-a)/2]}], 1], GCD@@#1>1&]]
PROG
(PARI) a(n) = if(n==0, return(0)); cn = factorback(factor(n)[, 1]); d = divisors(cn); -sum(i = 2, #d, round((n/d[i])^2/12) * (-1)^omega(d[i])) \\ David A. Corneth, Aug 24 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Amarnath Murthy, Apr 07 2003
EXTENSIONS
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 20 2003 and Dean Hickerson, Apr 22 2003
STATUS
approved