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A322608
Values of k such that (product of squarefree numbers <= k) / (sum of squarefree numbers <= k) is an integer.
3
1, 3, 11, 14, 17, 21, 23, 33, 34, 37, 46, 47, 55, 58, 59, 61, 62, 67, 69, 73, 82, 83, 87, 94, 95, 97, 101, 106, 107, 109, 114, 115, 119, 123, 127, 133, 134, 141, 146, 151, 157, 158, 159, 161, 165, 166, 173, 181, 187, 197, 202, 203, 210, 218, 219, 223, 226, 230
OFFSET
1,2
LINKS
EXAMPLE
3 is in the sequence because (1*2*3)/(1+2+3) = 1.
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.
MAPLE
with(numtheory): P:=proc(q) local a, b, c, n; a:=1; b:=0; c:=[];
for n from 1 to q do if issqrfree(n) then a:=a*n; b:=b+n;
if frac(a/b)=0 then c:=[op(c), n];
fi; fi; od; op(c); end: P(60);
MATHEMATICA
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 *)
CROSSREFS
Cf. A005117, A051838, A111059, A116536, A141092, A173143, A322607 (values of the quotient), A347690 (numbers of terms in the numerators).
Sequence in context: A228237 A186078 A224857 * A063963 A101585 A115214
KEYWORD
nonn,easy
AUTHOR
Paolo P. Lava, Dec 20 2018
EXTENSIONS
Definition corrected by N. J. A. Sloane, Sep 19 2021 at the suggestion of Harvey P. Dale.
STATUS
approved