A390718 - OEIS

%I #13 Nov 16 2025 10:10:42

%S 2,4,15,16,18,39,55,66,87,98,140,168,183,189,200,225,240,247,256,270,

%T 288,295,322,324,354,418,442,460,552,583,621,748,799,943,1064,1197,

%U 1255,1352,1425,1484,1506,1520,1521,1527,1634,1710,1785,1824,1904,1922,2052,2071,2120,2125,2142,2145,2288

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

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

%H Robert Israel, <a href="/A390718/b390718.txt">Table of n, a(n) for n = 1..10000</a>

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

%p filter:= proc(n) local t,s;

%p   t:= add(s[1]*s[2],s=ifactors(n)[2]);

%p   t = 2^padic:-ordp(t,2)

%p end proc:

%p select(filter, [$1..10^4]);

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

%Y Cf. A000079, A001414.

%K nonn

%O 1,1

%A _Will Gosnell_ and _Robert Israel_, Nov 16 2025