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A094268 Starting term of smallest consecutive n-tuples of abundant numbers. 1
0, 12, 5775, 171078830 (list; graph; refs; listen; history; text; internal format)
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 4-tuple 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), 156-157.

LINKS

Table of n, a(n) for n=0..3.

Paul Erdős, Note on consecutive abundant numbers, J. London Math. Soc. 10, 128-131 (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,changed

AUTHOR

Lekraj Beedassy, Jun 02 2004

STATUS

approved

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Last modified May 29 21:28 EDT 2017. Contains 287257 sequences.