|
%I #6 Jan 09 2018 12:32:19
%S 1,2,3,5,6,7,8,11,13,14,15,17,18,19,20,24,25,28,29,31,32,33,34,38,40,
%T 41,44,46,47,48,49,54,55,56,57,62,63,64,65,68,69,70,71,73,75,76,77,83,
%U 85,89,90,92,93,100,101,104,105,106,107,109,110,111,113,119,120,121,122
%N Number of pairs (b,c) with the same prime factors, 1<=b<=c<=n.
%C If pairs are restricted to b<c, we get the variant 0, 0, 0, 1, 1, 1, 1, 3, 4, 4, 4, 5, 5, 5, 5, 8, 8, 10, 10, 11, 11, 11, 11, 14, 15,...
%H Charles R Greathouse IV, <a href="/A140661/b140661.txt">Table of n, a(n) for n = 1..10000</a>
%H P. Erdos and T. Motzkin, <a href="http://www.jstor.org/stable/2324351">Density of pairs with same prime factors</a>, Am. Math. Month. vol 97 no 10 (1990) p 937, problem 5735.
%e a(16)=24 counts the 16 pairs (b,b) with 1<=b<=16 plus the 8 pairs (2,4), (2,8), (2,16), (4,8), (4,16), (8,16), (3,9), (6,12).
%o (PARI) samepf(m,n)=my(g=gcd(m,n),t=g); m/=g; while((t=gcd(t,m))>1, m/=t); if(m!=1, return(0)); t=g; while((t=gcd(t,n))>1, n/=t); n==1
%o a(n)=sum(b=1,n, sum(c=b,n, samepf(b,c))) \\ _Charles R Greathouse IV_, Jan 09 2018
%Y Partial sums of A008479.
%K easy,nonn
%O 1,2
%A _R. J. Mathar_, Jul 11 2008
|
