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%I #19 Apr 07 2024 05:42:10
%S 1,1,2,24,720,4480,3628800,1925,479001600,387459072,20922789888000,
%T 6402373705728000,5516784599040000,1124000727777607680000,
%U 135277939046250,24817936069329577574400,553211880832106496000000
%N Integers of the form k*k!/A062758(k) in the order they appear in A069149, where A062758(k) is the product of squares of divisors of k.
%t Rest[Select[Table[k! k/(Times@@Divisors[k])^2,{k,30}],IntegerQ]] (* _Harvey P. Dale_, Oct 17 2020 *)
%t Select[(# * #! / #^DivisorSigma[0, #]) & /@ Range[1, 30], IntegerQ] (* _Amiram Eldar_, Jul 16 2022 *)
%o (PARI) for(n=1,30,if((n*(n!))%(n^numdiv(n))==0,print1((n*(n!))/(n^numdiv(n)),",")))
%Y Cf. A062758, A069149.
%K easy,nonn
%O 1,3
%A _Benoit Cloitre_, Apr 08 2002
%E Name clarified by _Amiram Eldar_, Jul 16 2022
%E Missing a(1)=1 inserted by _Sean A. Irvine_, Apr 06 2024
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