A355497 Numbers k such that x^2 - s*x + p has only integer roots, where s and p denote the sum and product of the digits of k respectively.
0, 4, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80
Offset: 1
Examples
k = 14 is a term, since the sum of the digits of 14 is 5, the product of the digits of 14 is 4 and the roots 1 and 4 of x^2 - 5x + 4 are all integers.
Links
- Jean-Marc Rebert, Table of n, a(n) for n = 1..3002
Crossrefs
Programs
-
Mathematica
kmax=80;kdig:=IntegerDigits[k]; s:=Total[kdig]; p:=Product[Part[kdig,i],{i,Length[kdig]}]; a:={};For[k=0,k<=kmax,k++,If[Element[x/.Solve[x^2-s*x+p==0,x],Integers],AppendTo[a,k]]]; a (* Stefano Spezia, Jul 06 2022 *) -
PARI
is(n)=my(v=if(n,digits(n),[0])); issquare(vecsum(v)^2-4*vecprod(v))
Formula
a(n) = n + O(n^k) where k = log(9)/log(10) = 0.95424.... - Charles R Greathouse IV, Jul 07 2022
Comments