A362948 - OEIS

%I #12 Jul 27 2023 15:21:49

%S 5,6,12,18,24,25,36,48,54,72,96,108,125,144,162,192,216,288,324,384,

%T 432,486,576,625,648,768,864,972,1152,1296,1458,1536,1728,1944,2304,

%U 2592,2916,3072,3125,3456,3888,4374,4608,5184,5832,6144,6912,7776,8748,9216,10368,11664,12288

%N Numbers whose sum of (distinct) prime divisors (A008472) equals 5.

%H Amiram Eldar, <a href="/A362948/b362948.txt">Table of n, a(n) for n = 1..1000</a>

%F Union of A000351 = {5^k ; k > 0} and A033845 = {2^j*3^k, j,k > 0}.

%F Sum_{n>=1} 1/a(n) = 3/4. - _Amiram Eldar_, Jul 27 2023

%t seq[max_] := Union[Join[5^Range[Floor[Log[5, max]]], Flatten@ Table[2^i*3^j, {i, 1, Log2[max]}, {j, 1, Log[3, max/2^i]}]]]; seq[13000] (* _Amiram Eldar_, Jul 27 2023 *)

%o (PARI) select( {is_A362948(n)=vecsum(factor(n,0)[,1])==5}, [1..11^4]) \\ alternatively: [n | n<-[1..11^4], A008472(n)==5]

%Y Cf. A008472 (sopf), A000351 (5^n), A033845 (2^m*3^n).

%K nonn,easy

%O 1,1

%A _M. F. Hasler_, Jul 20 2023