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Number of distinct differences between consecutive divisors of n! (ordered by size).
2

%I #17 Jun 15 2024 05:49:32

%S 0,0,1,2,4,9,15,27,44,72,116,230,379,716,1154,1858,2589,5014,7299,

%T 15276,21901,33146,52298,102918,136647,200669,327572,432396,596869,

%U 1220172,1603092,3074018,3752018,5433507,8555035,11952469,14590378,30158257,46318453,66458379

%N Number of distinct differences between consecutive divisors of n! (ordered by size).

%F a(n) = A060682(n!).

%e For n = 4, n! = 24; divisors = {1,2,3,4,6,8,12,24}; differences = {1,1,1,2,2,4,12}, distinct differences = {1,2,4,12}, so a(4) = 4.

%t a[n_ ] := Length[Union[Drop[d=Divisors[n! ], 1]-Drop[d, -1]]]

%t Table[Length[Union[Differences[Divisors[n!]]]],{n,0,40}] (* _Harvey P. Dale_, Nov 22 2021 *)

%o (PARI) a(n) = {my(v = List(), d1 = 1); fordiv(n!, d, if(d > 1, listput(v, d-d1); d1 = d)); #Set(v);} \\ _Amiram Eldar_, Jun 15 2024

%Y Cf. A000142, A060682, A060738, A060742.

%K nonn

%O 0,4

%A _Labos Elemer_, Apr 25 2001

%E Edited by _Dean Hickerson_, Jan 22 2002

%E More terms from _Ryan Propper_, Mar 22 2006

%E a(37)-a(39) from _Amiram Eldar_, Jun 15 2024