A172248 - OEIS

%I #5 Aug 23 2020 15:55:51

%S 2,3,4,5,6,8,9,10,12,14,16,18,20,22,24,26,27,28,30,32,33,34,36,38,42,

%T 44,45,46,48,50,51,52,54,56,60,62,64,66,68,69,70,72,74,75,76,78,80,81,

%U 82,84,86,87,88,90,92,94,96,98,100,102,104,105,106,108,110,112,114,116,118

%N Numbers n such that there do not exist two ways of writing n = a+b with a<=b, gcd(n,a,b)=1, and the same value of N(a,b,n) = product of distinct prime divisors of a*b*n.

%C Number of partitions n as sum a + b such that a<=b and gcd(a,b,n)=1 is given in A023022

%C Number of partitions having distinct values of N(a,b,n) is given in A172245

%C Number of partitions having the same values of N(a,b,n) is given in A172247

%C Numbers n for which all partitions have different value of N(a,b,n) are given in A172248.

%e 7 doesn't belong to this sequence because for 7 we have two partitions 7=1+6 and 7=3+4 with that same values of N(a,b,n) respectively 1*2*3*7=42 and 2*3*7=42.

%Y Cf. A023022, A172245, A172246, A172247.

%K nonn

%O 2,1

%A _Artur Jasinski_, Jan 29 2010

%E Edited by _N. J. A. Sloane_, Aug 23 2020