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%I #23 Jul 07 2022 08:12:13
%S 1,2,3,5,7,9,11,12,13,15,17,19,21,23,24,25,27,29,30,31,32,33,35,36,37,
%T 39,40,41,43,45,47,48,49,50,51,53,54,55,56,57,59,60,61,63,64,65,67,69,
%U 70,71,72,73,75,77,79,80,81,83,84,85,87,88,89,90,91,93,95,96,97,98,99
%N Numbers k such that k*k!/A062758(k) is an integer where A062758(k) is the product of squares of divisors of k.
%C Also numbers k such that k! is divisible by k ^ (tau(k) - 1). - _David A. Corneth_, Apr 23 2018
%H Ivan Neretin, <a href="/A069149/b069149.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Range[100], Divisible[#!*#, Times @@ Divisors[#]^2] &] (* _Ivan Neretin_, Apr 22 2018 *)
%t Select[Range[100], Divisible[#!, #^(DivisorSigma[0, #] - 1)] &] (* _Amiram Eldar_, Jul 07 2022 *)
%o (PARI) for(n=1, 320, if((n*(n!))%(n^numdiv(n))==0, print1(n, ", ")))
%o (PARI) is(n) = {my(f = factor(n), qdiv = numdiv(f)); for(i = 1, #f~, cn = n; t = 0; while(cn \= f[i,1], t += cn); if(t < f[i,2] * (qdiv - 1), return(0))); 1} \\ _David A. Corneth_, Apr 27 2018
%Y Complement of A069148.
%Y Cf. A001563 (n*n!), A062758.
%K easy,nonn
%O 1,2
%A _Benoit Cloitre_, Apr 08 2002
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