A172247 - OEIS

A172247

Numbers k for which there are at least 2 partitions k = x+y with x<=y and gcd(x,y,k)=1 having the same value N(x,y,n) defined as the product of distinct prime divisors of x*y*n.

%I #11 Sep 01 2019 08:44:02

%S 7,11,13,15,17,19,21,23,25,29,31,35,37,39,40,41,43,47,49,53,55,57,58,

%T 59,61,63,65,67,71,73,77,79,83,85,89,91,93,95,97,99,101,103,107,109,

%U 111,113,115,117,119,121,123,125,127,129,131,133,136,137,139,143,145,147

%N Numbers k for which there are at least 2 partitions k = x+y with x<=y and gcd(x,y,k)=1 having the same value N(x,y,n) defined as the product of distinct prime divisors of x*y*n.

%e 7 is a term because we have two partitions 7=1+6 and 7=3+4 with same value of N(a,b,n) respectively 1*2*3*7=42 and 2*3*7=42.

%o (PARI) N(x, y, z) = vecprod(factor(x*y*z)[,1]);

%o isok(k) = {my(v = vector(0)); for (x=1, (k-1)\2, my(y = k-x); if (gcd(n, gcd(x, y)) == 1, v = concat(v, N(x, y, k)););); #v != #vecsort(v,,8);} \\ _Michel Marcus_, Sep 01 2019

%Y Cf. A023022, A172245, A172246, A172248.

%K nonn

%O 1,1

%A _Artur Jasinski_, Jan 29 2010

%E Edited by _Michel Marcus_, Sep 01 2019