A390718 Numbers k whose sum of prime factors (with multiplicity) is a power of 2.

2, 4, 15, 16, 18, 39, 55, 66, 87, 98, 140, 168, 183, 189, 200, 225, 240, 247, 256, 270, 288, 295, 322, 324, 354, 418, 442, 460, 552, 583, 621, 748, 799, 943, 1064, 1197, 1255, 1352, 1425, 1484, 1506, 1520, 1521, 1527, 1634, 1710, 1785, 1824, 1904, 1922, 2052, 2071, 2120, 2125, 2142, 2145, 2288

Offset

1,1

Comments

If k is a term, then so is k^2.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 15 is a term because 15 = 3 * 5 and 3 + 5 = 8 = 2^3.

Maple

filter:= proc(n) local t, s;
  t:= add(s[1]*s[2], s=ifactors(n)[2]);
  t = 2^padic:-ordp(t, 2)
end proc:
select(filter, [$1..10^4]);

Mathematica

q[k_] := k > 1 && (# == 2^IntegerExponent[#, 2])& @ (Plus @@ Times @@@ FactorInteger[k]); Select[Range[2300], q] (* Amiram Eldar, Nov 16 2025 *)

Crossrefs

Cf. A000079, A001414.

Sequence in context: A196239 A019543 A304568 * A271645 A265483 A357692

Adjacent sequences: A390715 A390716 A390717 * A390719 A390720 A390721

Keyword

nonn

Author

Will Gosnell and Robert Israel, Nov 16 2025

Status

approved