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A322608 Values of k such that (product of squarefree numbers <= k) / (sum of squarefree numbers <= k) is an integer.

%I A322608 #19 Sep 19 2021 15:11:13
%S A322608 1,3,11,14,17,21,23,33,34,37,46,47,55,58,59,61,62,67,69,73,82,83,87,
%T A322608 94,95,97,101,106,107,109,114,115,119,123,127,133,134,141,146,151,157,
%U A322608 158,159,161,165,166,173,181,187,197,202,203,210,218,219,223,226,230
%N A322608 Values of k such that (product of squarefree numbers <= k) / (sum of squarefree numbers <= k) is an integer.
%H A322608 Amiram Eldar, <a href="/A322608/b322608.txt">Table of n, a(n) for n = 1..10000</a>
%e A322608 3 is in the sequence because (1*2*3)/(1+2+3) = 1.
%e A322608 11 is in the sequence because (1*2*3*5*6*7*10*11)/(1+2+3+5+6+7+10+11) = 138600/45 = 3080.
%p A322608 with(numtheory): P:=proc(q) local a,b,c,n; a:=1; b:=0; c:=[];
%p A322608 for n from 1 to q do if issqrfree(n) then a:=a*n; b:=b+n;
%p A322608 if frac(a/b)=0 then c:=[op(c),n];
%p A322608 fi; fi; od; op(c); end: P(60);
%t A322608 seq = {}; sum = 0; prod = 1; Do[If[SquareFreeQ[n], sum += n; prod *= n; If[Divisible[prod, sum], AppendTo[seq, n]]], {n, 1, 230}]; seq (* _Amiram Eldar_, Mar 05 2021 *)
%Y A322608 Cf. A005117, A051838, A111059, A116536, A141092, A173143, A322607 (values of the quotient), A347690 (numbers of terms in the numerators).
%K A322608 nonn,easy
%O A322608 1,2
%A A322608 _Paolo P. Lava_, Dec 20 2018
%E A322608 Definition corrected by _N. J. A. Sloane_, Sep 19 2021 at the suggestion of _Harvey P. Dale_.