A140661 Number of pairs (b,c) with the same prime factors, 1<=b<=c<=n.

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, 41, 44, 46, 47, 48, 49, 54, 55, 56, 57, 62, 63, 64, 65, 68, 69, 70, 71, 73, 75, 76, 77, 83, 85, 89, 90, 92, 93, 100, 101, 104, 105, 106, 107, 109, 110, 111, 113, 119, 120, 121, 122

Offset: 1

Author

R. J. Mathar, Jul 11 2008

Keywords

• easy
• nonn

Comments

If pairs are restricted to b

Examples

			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).
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
• P. Erdos and T. Motzkin, Density of pairs with same prime factors, Am. Math. Month. vol 97 no 10 (1990) p 937, problem 5735.

Crossrefs

Partial sums of A008479.

Programs

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
a(n)=sum(b=1,n, sum(c=b,n, samepf(b,c))) \\ Charles R Greathouse IV, Jan 09 2018

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