A172245 a(n) = number of ways of writing n = i+j such that i<=j, gcd(i,j,n)=1, and the values of N(i,j,n) are distinct, where N(i,j,n) = product of distinct prime divisors of i*j*n.

0, 1, 1, 1, 2, 1, 2, 2, 3, 2, 4, 2, 5, 3, 3, 4, 7, 3, 7, 4, 5, 5, 8, 4, 8, 6, 9, 6, 13, 4, 12, 8, 10, 8, 10, 6, 16, 9, 11, 7, 18, 6, 19, 10, 12, 11, 19, 8, 18, 10, 16, 12, 23, 9, 17, 12, 17, 13, 27, 8, 26, 15, 17, 16, 21, 10, 30, 16, 22, 12, 29, 12, 30, 18, 20, 18, 26, 12, 34, 16, 27, 20, 38

Offset

1,5

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

a(5)=2 because we have two partitions 5=1+4 and 5=2+3 with different values of N(i,j,n), 1*2*5=10 and 2*3*5=30.

Prog

(PARI) a(n) = {l = List(); for(i = 1, n\2, if(gcd([i, (n-i), n]) == 1, listput(l, factorback(factor(i*(n-i)*n)[, 1])))); #Set(l)} \\ David A. Corneth, Aug 25 2020

Crossrefs

Number of partitions n = sum a + b such that a<=b, gcd(a,b,n)=1, see A023022

Cf. A172246.

Numbers n for which exist cases with that same value of function N(a,b,n), see A172247

Numbers n for which all partitions have different value of function N(a,b,n), see A172248.

Sequence in context: A260412 A360566 A283451 * A351005 A238781 A319439

Adjacent sequences: A172242 A172243 A172244 * A172246 A172247 A172248

Keyword

nonn,easy

Author

Artur Jasinski, Jan 29 2010

Extensions

Edited by N. J. A. Sloane, Aug 25 2020

a(1) = 0 prepended by David A. Corneth, Aug 25 2020

Status

approved