A140688 List of numbers which are both amicable and friendly.

12285, 67095, 71145, 87633, 142310

Offset: 1

Author

Walter Nissen, Jul 11 2008

Keywords

• more
• nonn

Comments

There are almost certainly many other amicables both within and without the displayed range which also are friendly, but they have not yet been identified.

The usual OEIS policy is to display sequences only as far as they are known to be complete. How far is this sequence known to be complete? - N. J. A. Sloane, Jul 12 2008. The answer appears to be that nothing is known for certain. It may well be that 12285 is not even the first term! - N. J. A. Sloane, Dec 04 2008

It is not known if the two smallest amicable numbers, 220 and 284, are friendly. In fact it is not even known if 10 is friendly. - Walter Nissen, Dec 02 2008

The following numbers are all known to be members of this sequence: 12285, 67095, 71145, 87633, 142310, 525915, 863835, 947835, 1125765, 1798875, 3606850, 5357625, 5684679, 5730615, 6088905, 9206925, 9478910, 9491625, 10634085, 12361622, 13671735, 14426230, 17041010, 17257695, 17754165, 20308995, 20955645, 22227075, 22508145, 23111055, 23389695, 25132545, 34765731, 35115795, 36939357, 43266285, 53011395, 66595130, 74769345, 80422335, 82824255, 82977345, 84591405. - Dean Hickerson, Dec 02 2008 (communicated by Walter Nissen). However, until we have more definite information about the correctness of the first five terms (there could be additional terms less than 142310), there is no point in adding these terms to the "DATA" line. - N. J. A. Sloane, Nov 23 2011

Examples

			(69615, 87633) are an amicable pair with sigma = 157248. { 14445, 87633 } are a friendly pair of abundancy = 192/107. Therefore 87633 is a member of the sequence.
The smallest friend of 3606850 is 7521154875.
		

References

• Dean Hickerson, "Re: Friendly number", post to sci.math newsgroup, 2000, available through groups.google.com.
• Ore, Oystein, Number Theory and Its History, McGraw-Hill, 1948, reprinted 1988, section 5-3, pp 96-100.

Links

• Claude W. Anderson and Dean Hickerson, Problem 6020: Friendly Integers, Amer. Math. Monthly 84 (1977) pp. 65-66.
• Walter Nissen, Abundancy : Some Resources
• Walter Nissen, Primitive Friendly Integers and Exclusive Multiples
• J. O. M. Pedersen, Known Amicable Pairs [Broken link]
• Eric Weisstein's World of Mathematics, Friendly Pair

Crossrefs

Cf. A063990, A074902.

Extensions

Edited by N. J. A. Sloane, Dec 04 2008 and Nov 23 2011