cp's OEIS Frontend

A151991 Numbers k with the property that (k-x)*(k-y)*(k-z) = x*y*z has no integer solutions 0 < x,y,z < k.

%I A151991 #16 Aug 08 2023 12:19:34
%S A151991 1,3,5,7,9,11,13,17,19,21,23,25,27,29,31,33,37,39,41,43,47,49,51,53,
%T A151991 57,59,61,67,69,71,73,79,81,83,87,89,93,95,97,101,103,107,109,111,113,
%U A151991 115,121,123,125,127,129,131,133,137,139,141,145,147,149,151,155,157,159
%N A151991 Numbers k with the property that (k-x)*(k-y)*(k-z) = x*y*z has no integer solutions 0 < x,y,z < k.
%C A151991 All odd primes are terms of this sequence.
%e A151991 15 is not a term of this sequence because (15-x)*(15-y)*(15-z) = x*y*z has the solution (5,5,12).
%o A151991 (Python)
%o A151991 def exis(n):
%o A151991     for x in range(1,n):
%o A151991         for y in range(x+1):
%o A151991             for z in range(y+1):
%o A151991                 if x*y*z==(k-x)*(k-y)*(k-z):
%o A151991                     return True
%o A151991     return False
%o A151991 for k in range(1, 200, 2):
%o A151991     if not exis(k):
%o A151991         print(str(k), end=',')
%o A151991 (PARI) is(n)=for(x=1,n-1,for(y=1,x, my(t=(n-x)*(n-y),z=t*n/(x*y+t)); if(denominator(z)==1 && 0 < z && z < n, return(0)))); 1 \\ _Charles R Greathouse IV_, Dec 09 2014
%Y A151991 Cf. A065091 (odd primes).
%K A151991 nonn
%O A151991 1,2
%A A151991 Nurdin Takenov (greanvert(AT)gmail.com), Sep 14 2009
%E A151991 Edited by _Charles R Greathouse IV_, Dec 09 2014