

A094268


Starting term of smallest consecutive ntuples of abundant numbers.


2




OFFSET

0,2


COMMENTS

The triple 171078830, 171078831, 171078832 was apparently found by Laurent Hodges and Michael Reid in 1995.
The starting term of the smallest consecutive 4tuple of abundant numbers is at most 141363708067871564084949719820472453374  Bruno Mishutka (bruno.mishutka(AT)googlemail.com), Nov 01 2007
Paul Erdős showed that there are two absolute constants c1, c2 such that for all large n there are at least c1 log log log n but not more than c2 log log log n consecutive abundant numbers less than n.  Bruno Mishutka (bruno.mishutka(AT)googlemail.com), Nov 01 2007
The term a(0) = 0 is included to avoid the warning messages triggered by sequences with fewer than four terms.  N. J. A. Sloane, Nov 07 2007


REFERENCES

J.M. De Koninck and A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 771, pp. 98, 327, Ellipses, Paris, 2004.
S. Kravitz, Three Consecutive Abundant Numbers, Journal of Recreational Mathematics, 26:2 (1994), 149. Solution by L. Hodges and M. Reid, JRM, 27:2 (1995), 156157.


LINKS

Table of n, a(n) for n=0..3.
Paul Erdős, Note on consecutive abundant numbers, J. London Math. Soc. 10, 128131 (1935).
Carlos Rivera, Puzzle 878. Consecutive abundant integers


CROSSREFS

Cf. A005105, A005231.
Sequence in context: A230749 A003793 A171669 * A208865 A012607 A167072
Adjacent sequences: A094265 A094266 A094267 * A094269 A094270 A094271


KEYWORD

hard,more,nonn


AUTHOR

Lekraj Beedassy, Jun 02 2004


STATUS

approved



