A360140 Odd amicable pairs with only one member divisible by 3.

445953248528881275, 659008669204392325, 748174019876835825, 906104451346869775, 1097581690986390225, 1615281291559017775, 1281431098689616875, 1769164614201263125, 1968382462511781225, 2982869282783783575, 1993991197249826775, 2901232579265245225, 2247817805416685775, 2726235257034514225

Offset: 1

Author

Zoltan Galantai, Jan 26 2023

Keywords

• nonn

Comments

In these pairs only the smaller number is divisible by 3 and both the smaller and the larger number are divisible by 5, 7, and 25. These pairs prove that there are odd amicable pairs where only one of the numbers is divisible by 3.

Examples

			(445953248528881275, 659008669204392325) belongs to the sequence since the smaller number is divisible by 3 and the larger is not. The (12285, 14595) pair is not a part of the sequence, since both of its members are divisible by 3.
		

References

• Richard K. Guy, Unsolved Problems in Number Theory. Springer, 2004, page 88.

Links

• S. Battiato and W. Borho, Are There Odd Amicable Numbers Not Divisible by Three, Mathematics of Computation, Apr., 1988, Vol. 50, No. 182, pp. 633-637.
• S. Chernykh, Amicable pairs where the two members have different smallest prime factors, January 30th, 2016.
• Zoltan Galantai, List of 31 known pairs

Crossrefs

Cf. A259180, A002025, A002046, A262623.