OFFSET
1,1
COMMENTS
I call the numbers in this sequence "just numbers", since they "fairly" allow both their odd and even aliquot part sums to divide them.
Vladeta Jovovic of Belgrade University proved that every just number not equal to 4 is twice a perfect number. The proof appears in the link.
LINKS
Joseph L. Pe, The Justice of Numbers: A Problem Proposal, Nov 21 2001
EXAMPLE
The sum of the odd aliquot parts of 4 is 1 and the sum of the even aliquot parts of 4 is 2; both sums divide 4. The sum of the odd aliquot parts of 12 is 3 + 1 = 4 and the sum of the even aliquot parts of 12 is 6 + 4 + 2 = 12; both sums divide 12.
MATHEMATICA
Do[d = Drop[ Divisors[n], -1]; l = Length[d]; ev = 0; od = 1; k = 2; While[k <= l, If[ EvenQ[ d[[k]]], ev = ev + d[[k]], od = od + d[[k]]]; k++ ]; If[ IntegerQ[n/ev] && IntegerQ[n/od], Print[n]], {n, 2, 10^6, 2} ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Joseph L. Pe, Nov 13 2001
EXTENSIONS
More terms from Robert G. Wilson v, Oct 10 2002
STATUS
approved