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%I #16 Sep 08 2022 08:45:40
%S 0,0,0,3,29,225,1669,14245,118705,1118001,11705019,144091717,
%T 1738439017,24817157329,355309322689,5378578597729,86081749391905,
%U 1570394279028289,28281459220178401,572031558109560385,11458497230555053681
%N Sum of proper divisors minus the number of proper divisors of n!.
%C a(n) is the sum of proper divisors minus the number of proper divisors of factorial number A000142(n).
%H G. C. Greubel, <a href="/A153825/b153825.txt">Table of n, a(n) for n = 0..500</a>
%F a(n) = A153824(n) - A153823(n) = A152770(A000142(n)).
%p with(numtheory): seq(sigma(factorial(n))-factorial(n)-tau(factorial(n))+1, n = 0 .. 22); # _Emeric Deutsch_, Jan 07 2009
%t Table[DivisorSigma[1,n!]-n!-(DivisorSigma[0,n!]-1),{n,0,20}] (* _Harvey P. Dale_, Jan 14 2012 *)
%o (Magma) [DivisorSigma(1,Factorial(n)) - Factorial(n) - (DivisorSigma(0,Factorial(n))-1): n in [0..20]]; // _Vincenzo Librandi_, Aug 31 2016
%o (PARI) a(n) = (sigma(n!) - n!) - (numdiv(n!) - 1); \\ _Michel Marcus_, Aug 31 2016
%Y Cf. A000005, A000142, A000203, A001065, A032741, A062569, A152770, A153823, A153824.
%K nonn
%O 0,4
%A _Omar E. Pol_, Jan 02 2009
%E Extended by _Emeric Deutsch_, Jan 07 2009
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