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

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

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A322605 A322606 A322607 * A322609 A322610 A322611

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