A339666 Number of nonempty subsets of divisors of n whose root-mean-square is an integer.

1, 2, 2, 3, 2, 4, 3, 4, 3, 4, 2, 6, 2, 6, 4, 5, 2, 6, 2, 6, 6, 4, 2, 8, 3, 4, 4, 9, 2, 8, 2, 6, 4, 4, 7, 9, 2, 4, 4, 12, 3, 12, 2, 6, 7, 4, 2, 12, 5, 6, 4, 6, 2, 8, 5, 12, 4, 4, 2, 26, 2, 4, 9, 7, 4, 8, 2, 6, 4, 14, 2, 12, 2, 4, 6, 6, 6, 8, 2, 24, 5, 6, 2, 22

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Root-Mean-Square

Index entries for sequences related to divisors of numbers

Example

a(14) = 6 subsets: {1}, {2}, {7}, {14}, {1, 7} and {2, 14}.

Maple

a:= proc(n) option remember; uses numtheory; local l, b;
      l, b:= sort([divisors(n)[]]),
      proc(i, s, c) option remember;
        `if`(i=0, `if`(c>0 and issqr(s/c), 1, 0),
         b(i-1, s, c)+b(i-1, s+l[i]^2, c+1))
      end; forget(b); b(nops(l), 0$2)
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Sep 30 2022

Mathematica

a[n_] := a[n] = Module[{b, l = Divisors[n]}, b[i_, s_, c_] := b[i, s, c] = If[i == 0, If[c > 0 && IntegerQ @ Sqrt[s/c], 1, 0], b[i-1, s, c]+b[i-1, s+l[[i]]^2, c+1]]; b[Length[l], 0, 0]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Oct 13 2022, after Alois P. Heinz *)

Crossrefs

Cf. A027750, A100587, A339454, A339663, A339664, A339665.

Sequence in context: A359360 A323164 A363685 * A318881 A280338 A339147

Adjacent sequences: A339663 A339664 A339665 * A339667 A339668 A339669

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 11 2020

Status

approved