login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A060742 Number of divisors of n! which are also differences between consecutive divisors of n! (ordered by size). 6
0, 0, 1, 2, 4, 9, 15, 27, 41, 68, 111, 218, 328, 624, 929, 1518, 2016, 3689, 4965, 9252, 13177, 20016, 30697, 56749, 69434, 94242, 149558, 190292, 258370, 492924, 615063, 1149403, 1325124, 1841343, 2737190, 3592273 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..35.

D. Berend et al., Gaps between consecutive divisors of factorials, Ann. Inst. Fourier, 43 (3) (1993), 569-583.

EXAMPLE

For n=5, n!=120; divisors={1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120}; differences={1,1,1,1,1,2,2,2,3,5,4,6,10,20,60}; intersection={1,2,3,4,5,6,10,20,60}, so a(5)=9.

MAPLE

f:= proc(n) local D, L;

D:= numtheory:-divisors(n!);

L:= sort(convert(D, list));

nops(convert(L[2..-1]-L[1..-2], set) intersect D);

end proc:

map(f, [$0..34]); # Robert Israel, Jul 03 2017

MATHEMATICA

a[n_ ] := Length[Intersection[Drop[d=Divisors[n! ], 1]-Drop[d, -1], d]]

CROSSREFS

Cf. A000142, A027423, A060737, A060738, A060741.

Sequence in context: A157254 A080004 A176915 * A060737 A266647 A085683

Adjacent sequences: A060739 A060740 A060741 * A060743 A060744 A060745

KEYWORD

nonn

AUTHOR

Labos Elemer, Apr 23 2001

EXTENSIONS

Edited by Dean Hickerson, Jan 22 2002

One more term from Robert G. Wilson v, Jan 29 2002

a(33)-a(35) from Robert Israel, Jul 03 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 14:59 EST 2022. Contains 358700 sequences. (Running on oeis4.)