This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A140661 #6 Jan 09 2018 12:32:19 %S A140661 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 A140661 41,44,46,47,48,49,54,55,56,57,62,63,64,65,68,69,70,71,73,75,76,77,83, %U A140661 85,89,90,92,93,100,101,104,105,106,107,109,110,111,113,119,120,121,122 %N A140661 Number of pairs (b,c) with the same prime factors, 1<=b<=c<=n. %C A140661 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 A140661 Charles R Greathouse IV, <a href="/A140661/b140661.txt">Table of n, a(n) for n = 1..10000</a> %H A140661 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 A140661 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 A140661 (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 A140661 a(n)=sum(b=1,n, sum(c=b,n, samepf(b,c))) \\ _Charles R Greathouse IV_, Jan 09 2018 %Y A140661 Partial sums of A008479. %K A140661 easy,nonn %O A140661 1,2 %A A140661 _R. J. Mathar_, Jul 11 2008