A060738 - OEIS

%I #17 Jun 15 2024 05:49:36

%S 0,0,0,0,0,0,0,0,3,4,5,12,51,92,225,340,573,1325,2334,6024,8724,13130,

%T 21601,46169,67213,106427,178014,242104,338499,727248,988029,1924615,

%U 2426894,3592164,5817845,8360196,10396523,21941765,33649653,48804040,61413482,124029358

%N Number of distinct differences between consecutive divisors (ordered by increasing magnitude) of n! which are not also divisors of n!.

%F a(n) = A060763(n!).

%e For n up to 7 all divisor differences of n! are also divisors of n!.

%e For n = 8, there are 3 divisor differences of 8! = 40320 which are not divisors of 8!, namely 27, 54 and 108.

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

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

%Y Cf. A000142, A027423, A060737, A060742, A060763.

%K nonn

%O 0,9

%A _Labos Elemer_, Apr 25 2001

%E Edited by _Dean Hickerson_, Jan 22 2002

%E More terms from _Sean A. Irvine_, Dec 21 2022

%E a(41) from _Amiram Eldar_, Jun 15 2024