

A181063


Smallest positive integer with a discrete string of exactly n consecutive divisors, or 0 if no such integer exists.


15



1, 2, 6, 12, 3960, 60, 420, 840, 17907120, 2520, 411863760, 27720, 68502634200, 447069823200, 360360, 720720, 7600186994400, 12252240, 9524356075634400, 81909462250455840, 1149071006394511200, 232792560, 35621201198229847200, 5354228880, 91351145008363640400
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

The word "discrete" is used to describe a string of consecutive divisors that is not part of a longer such string.
Does a(n) ever equal 0?


LINKS



EXAMPLE

a(5) = 3960 is divisible by 8, 9, 10, 11, and 12, but not 7 or 13. It is the smallest positive integer with a string of 5 consecutive divisors that is not part of a longer string.
The sequence of terms together with their divisors begins:
1: {1}
2: {1,2}
6: {1,2,3,6}
12: {1,2,3,4,6,12}
3960: {1,2,...,8,9,10,11,12,...,1980,3960}
60: {1,2,3,4,5,6,...,30,60}
420: {1,2,3,4,5,6,7,...,210,420}
840: {1,2,3,4,5,6,7,8,...,420,840}
(End)


MATHEMATICA

tav=Table[Length/@Split[Divisors[n], #2==#1+1&], {n, 10000}];
Table[Position[tav, i][[1, 1]], {i, Split[Union@@tav, #2==#1+1&][[1]]}] (* Assumes there are no zeros.  Gus Wiseman, Oct 16 2019 *)


CROSSREFS

The version taking only the longest run is A328449.
The longest run of divisors of n has length A055874(n).
Numbers whose divisors > 1 have no nonsingleton runs are A088725.
The number of successive pairs of divisors of n is A129308(n).


KEYWORD

nonn


AUTHOR



STATUS

approved



