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

1,2

Comments

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,...

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.

Example

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).

Prog

(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

Crossrefs

Partial sums of A008479.

Sequence in context: A284885 A094180 A116545 * A063966 A123030 A284836

Adjacent sequences: A140658 A140659 A140660 * A140662 A140663 A140664

Keyword

easy,nonn

Author

R. J. Mathar, Jul 11 2008

Status

approved