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%I #6 Oct 19 2014 15:42:30
%S 1575,2835,3465,4095,4725,5355,5775,5985,6435,6615,6825,7245,7875,
%T 8085,8505,9135,9765,10395,11025,11655,12285,12705,12915,13545,14175,
%U 14805,15015,15435,16065,16695,17325,17955,18585,19215,19305,19635,19845,20475,21105
%N Odd numbers k such that the product of factorials of proper divisors of k does not divide k!
%C Is every term a multiple of 15?
%e Let Q(n) = n!/(product of the proper divisors of n). Then Q(a(1)) = N/D, where
%e N = 5684447784292091153753490743683678065401858735042447947039489051000812450375
%e 96097513516069953368913418355291373745171485235214678313832004750769512243570213
%e 17329337171352254034549578081676132223379527381310854584384222707565139611863694
%e 30640235947065824459529570708496537565356400158201705547084883398448628433876851
%e 45027005261482010735089664203432206284363981438356549492398792517845833981953470
%e 11656242198592638046634626564224371702079154967385329347508423182940832991802020
%e 79729029554388862293013132314260080936743113826499242289158506713167932372780456
%e 35478273889560173970236977657583276028820238215910913046229649347260976100815721
%e 30514647760639026540100704923229175316918713642498606000080175020651282466288262
%e 98949351261557660288695788306642653729696037113284350082653527072196917361726113
%e 54899425631403773739526421814643000628257393623101868506322157155784868034570876
%e 94944795541518746296597484128788416505102809202721810698024533196028905603665016
%e 69160279455786632925907732365477717222525851009413148227878461914230042744382703
%e 86503762563952079367594382974183048359869258795095100225724624706161418465202017
%e 63929456631534509078212894380900186189087478989553793461391475049200947755236771
%e 281068356116704064311250402286679067
%e and
%e D = 6449725440000.
%t d[n_] := Drop[Divisors[n], -1]!; p[n_] := Apply[Times, d[n]]
%t u = Select[Range[25000], ! IntegerQ[#!/p[#]] &]; (* A248693 *)
%t Select[u, OddQ[#] &] (* A248694 *)
%Y Cf. A248692, A027750.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Oct 12 2014
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