A233553 Amicable 5-tuples: (x1,...,x5) such that sigma(x1)=...=sigma(x5)=x1+...+x5. Groups of 5 subsequent terms list the five members in increasing size.

53542288800, 59509850400, 59999219280, 60074174160, 61695597600, 67154527440, 68763895200, 69626138400, 71957405520, 72598125600, 67509842400, 72747675000, 73605331800, 75710489400, 78953074200, 87113426400, 88410722400, 89398663200, 96058282320, 96369633360

Offset: 1

Author

M. F. Hasler, Dec 12 2013

Keywords

• nonn
• hard

Comments

The 5-tuple starting with 53542288800 was given by Donovan Johnson. The common value of sigma(x) is 294821130240.

A larger 5-tuple, (55766707476480, 56992185169920, 57515254917120, 57754372515840, 57829096765440), was found by Michel Marcus on Dec 09 2013. The common value of sigma(x) is 285857616844800.

A still larger example (227491164588441600, 228507506351308800, 229862628701798400, 230878970464665600, 243752632794316800), probably the first one to be published, had been found by Yasutoshi Kohmoto in 2008, cf. link to SeqFan post.

There are different definitions for amicable k-tuples, cf. link to MathWorld.

Links

• John Cerkan, Table of n, a(n) for n = 1..45
• John Cerkan, More terms, with gaps.
• Yasutoshi Kohmoto, Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v, SeqFan list, Nov 23 2008
• Yasutoshi Kohmoto, Sigma(x)=Sigma(y)=Sigma(z)=Sigma(u)=Sigma(v)=x+y+z+u+v, SeqFan list, Dec 09 2013
• Eric Weisstein's World of Mathematics, Amicable Triple.

Crossrefs

Cf. A273928, A273930, A273931, A273933, A273934, A273936 (5-tuples).

Cf. A036471 - A036474 and A116148 (quadruples).

Cf. A125490 - A125492 and A137231 (triples).

Extensions

More terms from John Cerkan, Jun 05 2016