Answer:
1) The sum of the odd square numbers less than 100 are all odd while the factor sums of non-square odd numbers are also always odd.
2) The sum of the even square numbers less than 100 are always odd while the sum of of non-square even numbers are not always odd.
Step-by-step explanation:
The odd square numbers are:
9,49,81
The factors are:
9={1,3,9}
Sum of factors of 9:1+3+9=13
The factors of 49 are:
49={1,7,49}
Sum of factors of 49 : 1+7+49=57
The factors of 81 are: {1,3,9,27,81}
Their sum:1+3+9+27+81=121
The non-square even numbers are:
2,6,8,10,12,14,....
Factors of 2:{1,2}
Sum of factors:1+2=3
Factors of 6: {1,2,3,6}
Sum of factors:1+2+3+6=12
Factors of 8: {1,2,4,8}
Sum: 1+2+4+8=15
Factors of 10:{1,2,5,10}
Sum: 1+2+5+10=18
Factors of 12:{1,2,3,4,6,12}
Sum:1+2+3+4+6+12=28
Factors of 14: {1,2,7,14}
Sum:1+2+7+14=24
Even square numbers less than 100 are:
4,16,36,64
Factors of 4={1,2,4}
Sum:1+2+4=7
Factors of 16: {1,2,4,8,16}
Sum : 1+2+4+8+16=31
Factors of 36: {1,2,3,4,6,9,12,18,36}
Sum : 1+2+3+4+6+9+12+18+36=91
The non-square odd numbers are:
3,5,7,11,....
Factors of 3:{1,3}
Sum : 1+3=4
Factors of 5: {1,5}
Sum: 1+5=6
Factors of 7:{1,7}
Sum of factors: 1+7=8
Factors of 15: {1,3,5,15}
Sum: 1+3+5+15=24
Factors of 21:{1,3,7,21}
Sum: 1+3+7+21=32
Factors of 27: {1,3,9,27}
Sum: 1+3+9+27=40
